Pub Date : 2024-11-12DOI: 10.1016/j.nuclphysb.2024.116740
Wei Chao , Jing-jing Feng , Huai-ke Guo , Tong Li
The discovery of gravitational waves (GWs) opens a new window for exploring the physics of the early universe. Identifying the source of GWs and their spectra at present turns out to be important tasks so as to assist the experimental detection of stochastic GW signal. In this paper, we investigate oscillations of the ultralight dark photon (ULDP) into GWs in the dark halo. Assuming dark matter is composed of the ULDP and there are primordial dark magnetic fields (PDMFs) arising from the axion inflation and/or the dark phase transition, then the ULDP can oscillate into the GW when it passes through an environment of PDMFs. We derive the local energy density of GWs in the galaxy cluster induced by the instaneous oscillation of ULDP in the PDMFs. These stochastic local GWs exhibit a pulse-like spectrum, with frequency depending on the mass of the ULDP, and can be detected in Pulsar Timing Arrays (PTAs) or future space-based interferometers. We also find that the low-frequency GW signal observed by the NANOGrav collaboration and other PTA experiments can be addressed by the oscillation of the ULDP in the PDMFs in the early universe.
{"title":"Oscillations of ultralight dark photon into gravitational waves","authors":"Wei Chao , Jing-jing Feng , Huai-ke Guo , Tong Li","doi":"10.1016/j.nuclphysb.2024.116740","DOIUrl":"10.1016/j.nuclphysb.2024.116740","url":null,"abstract":"<div><div>The discovery of gravitational waves (GWs) opens a new window for exploring the physics of the early universe. Identifying the source of GWs and their spectra at present turns out to be important tasks so as to assist the experimental detection of stochastic GW signal. In this paper, we investigate oscillations of the ultralight dark photon (ULDP) into GWs in the dark halo. Assuming dark matter is composed of the ULDP and there are primordial dark magnetic fields (PDMFs) arising from the axion inflation and/or the dark phase transition, then the ULDP can oscillate into the GW when it passes through an environment of PDMFs. We derive the local energy density of GWs in the galaxy cluster induced by the instaneous oscillation of ULDP in the PDMFs. These stochastic local GWs exhibit a pulse-like spectrum, with frequency depending on the mass of the ULDP, and can be detected in Pulsar Timing Arrays (PTAs) or future space-based interferometers. We also find that the low-frequency GW signal observed by the NANOGrav collaboration and other PTA experiments can be addressed by the oscillation of the ULDP in the PDMFs in the early universe.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1009 ","pages":"Article 116740"},"PeriodicalIF":2.5,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-08DOI: 10.1016/j.nuclphysb.2024.116736
Bhagya. R , Harsha Sreekumar , E. Harikumar , R.P. Malik
We perform the constraint analysis of a three (2 + 1)-dimensional (3D) field-theoretic example for Hodge theory (i) at the classical level within the ambit of Lagrangian formulation, and (ii) at the quantum level within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. We derive the conserved charges corresponding to the six continuous symmetries of our present theory. These six continuous summery transformations are the nilpotent (anti-)BRST and (anti-)co-BRST symmetries, a unique bosonic symmetry and the ghost-scale symmetry. It turns out that the Noether conserved (anti-)BRST charges are found to be non-nilpotent even though they are derived from the off-shell nilpotent versions of the continuous and infinitesimal (anti-)BRST symmetry transformations. We obtain the nilpotent versions of the (anti-)BRST charges from the non-nilpotent Noether (anti-)BRST charges and discuss the physicality criteria w.r.t. the latter to demonstrate that the operator forms of the first-class constraints (of the classical gauge theory) annihilate the physical states at the quantum level. This observation is consistent with Dirac's quantization conditions for the systems that are endowed with the constraints. We lay emphasis on the existence of a single (anti-)BRST invariant Curci-Ferrari (CF) type restriction in our theory and derive it from various theoretical angles.
{"title":"Constraints, conserved charges and extended BRST algebra for a 3D field-theoretic example for Hodge theory","authors":"Bhagya. R , Harsha Sreekumar , E. Harikumar , R.P. Malik","doi":"10.1016/j.nuclphysb.2024.116736","DOIUrl":"10.1016/j.nuclphysb.2024.116736","url":null,"abstract":"<div><div>We perform the constraint analysis of a three (2 + 1)-dimensional (3D) field-theoretic example for Hodge theory (i) at the <em>classical</em> level within the ambit of Lagrangian formulation, and (ii) at the <em>quantum</em> level within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. We derive the conserved charges corresponding to the <em>six</em> continuous symmetries of our present theory. These six continuous summery transformations are the nilpotent (anti-)BRST and (anti-)co-BRST symmetries, a unique bosonic symmetry and the ghost-scale symmetry. It turns out that the <em>Noether</em> conserved (anti-)BRST charges are found to be non-nilpotent even though they are derived from the off-shell nilpotent versions of the continuous and infinitesimal (anti-)BRST symmetry transformations. We obtain the nilpotent versions of the (anti-)BRST charges from the non-nilpotent <em>Noether</em> (anti-)BRST charges and discuss the physicality criteria w.r.t. the <em>latter</em> to demonstrate that the operator forms of the first-class constraints (of the <em>classical</em> gauge theory) annihilate the physical states at the quantum level. This observation is consistent with Dirac's quantization conditions for the systems that are endowed with the constraints. We lay emphasis on the existence of a <em>single</em> (anti-)BRST invariant Curci-Ferrari (CF) type restriction in our theory and derive it from various theoretical angles.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1009 ","pages":"Article 116736"},"PeriodicalIF":2.5,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-08DOI: 10.1016/j.nuclphysb.2024.116737
Carlos R. Ordóñez
I am gladly sharing a few anecdotes of my interactions with Steven Weinberg during many years, from my student days to more recent times.
我很高兴与大家分享我与史蒂文-温伯格多年交往的一些轶事，从我的学生时代到最近。
{"title":"Steven Weinberg remembrances","authors":"Carlos R. Ordóñez","doi":"10.1016/j.nuclphysb.2024.116737","DOIUrl":"10.1016/j.nuclphysb.2024.116737","url":null,"abstract":"<div><div>I am gladly sharing a few anecdotes of my interactions with Steven Weinberg during many years, from my student days to more recent times.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1009 ","pages":"Article 116737"},"PeriodicalIF":2.5,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-07DOI: 10.1016/j.nuclphysb.2024.116728
Rabia Saleem, Iqra Shahid, M. Israr Aslam, Abdul Wahab
This research paper used a newly proposed strategy for finding the exact inflationary solutions to the Friedman equations in the context of Rastall theory of gravity (RTG), which is known as constant-roll warm inflation (CRWI). The dissipative effects produced during WI are studied by introducing a dissipation factor , where Γ is the coefficient of dissipation. We establish the model to evaluate the inflaton field, effective potential requires to produce inflation, and entropy density. These physical quantities lead to developing the important inflationary observables like scalar/tensor power spectrum, scalar spectral index, tensor-to-scalar ratio, and running of spectral-index for two choices of obtained potential that are and . In this study, we focus on the effects of the theory parameter λ, CR parameter β, and dissipation factor Q (under a high dissipative regime for which Q=constant) on inflation, and are constrained to observe the compatibility of our model with Planck TT+lowP (2013), Planck TT, TE, EE+lowP (2015), Planck 2018 and BICEP/Keck 2021 bounds. The results are feasible and interesting up to the 2σ confidence level. Finally, we conclude that the CR technique produces significant changes in the early universe.
这篇研究论文采用了一种新提出的策略，在拉斯托尔引力理论（Rastall theory of gravity，RTG）的背景下找到弗里德曼方程的精确膨胀解，即所谓的恒定辊温膨胀（constant-roll warm inflation，CRWI）。通过引入耗散因子 Q=Γ3H，其中Γ是耗散系数，研究了 WI 过程中产生的耗散效应。我们建立模型来评估膨胀场、产生膨胀所需的有效势以及熵密度。这些物理量导致了重要的暴胀观测指标的发展，如标量/张量功率谱、标量谱指数、张量与标量之比，以及在 V0=0 和 V0≠0 两种获得的势的情况下谱指数的运行。在这项研究中，我们重点研究了理论参数λ、CR参数β和耗散因子Q（在Q=常数的高耗散机制下）对膨胀的影响，并受限于观察我们的模型与Planck TT+lowP（2013）、Planck TT、TE、EE+lowP（2015）、Planck 2018和BICEP/Keck 2021约束的兼容性。这些结果在 2σ 置信度以内都是可行和有趣的。最后，我们得出结论：CR 技术会使早期宇宙发生重大变化。
{"title":"Constant-roll warm inflation within Rastall gravity","authors":"Rabia Saleem, Iqra Shahid, M. Israr Aslam, Abdul Wahab","doi":"10.1016/j.nuclphysb.2024.116728","DOIUrl":"10.1016/j.nuclphysb.2024.116728","url":null,"abstract":"<div><div>This research paper used a newly proposed strategy for finding the exact inflationary solutions to the Friedman equations in the context of Rastall theory of gravity (RTG), which is known as constant-roll warm inflation (CRWI). The dissipative effects produced during WI are studied by introducing a dissipation factor <span><math><mi>Q</mi><mo>=</mo><mfrac><mrow><mi>Γ</mi></mrow><mrow><mn>3</mn><mi>H</mi></mrow></mfrac></math></span>, where Γ is the coefficient of dissipation. We establish the model to evaluate the inflaton field, effective potential requires to produce inflation, and entropy density. These physical quantities lead to developing the important inflationary observables like scalar/tensor power spectrum, scalar spectral index, tensor-to-scalar ratio, and running of spectral-index for two choices of obtained potential that are <span><math><msub><mrow><mi>V</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>0</mn></math></span> and <span><math><msub><mrow><mi>V</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≠</mo><mn>0</mn></math></span>. In this study, we focus on the effects of the theory parameter <em>λ</em>, CR parameter <em>β</em>, and dissipation factor <em>Q</em> (under a high dissipative regime for which <em>Q</em>=constant) on inflation, and are constrained to observe the compatibility of our model with Planck TT+lowP (2013), Planck TT, TE, EE+lowP (2015), Planck 2018 and BICEP/Keck 2021 bounds. The results are feasible and interesting up to the 2<em>σ</em> confidence level. Finally, we conclude that the CR technique produces significant changes in the early universe.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1009 ","pages":"Article 116728"},"PeriodicalIF":2.5,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-07DOI: 10.1016/j.nuclphysb.2024.116734
Jose M. Ladino , Carlos E. Romero-Figueroa , Hernando Quevedo
We study the thermodynamic properties of the Reissner-Nordström black hole with cosmological constant, expressed in terms of the curvature radius, using the approach of shadow thermodynamics and the formalism of geometrothermodynamics. We derive explicit expressions for the shadow radius in terms of the horizon, photon sphere, and observer radii. The phase transition structure turns out to strongly depend on the value of the curvature radius, including configurations with zero, one, or two phase transitions. We also analyze the black hole's microscopic structure and find differences between the approaches of thermodynamic geometry and geometrothermodynamics, which are due to the presence of the curvature radius. We impose the important condition that the black hole is a quasi-homogeneous thermodynamic system to guarantee the consistency of the geometrothermodynamic approach.
{"title":"Phase transitions, shadows, and microstructure of Reissner-Nordström-Anti-de-Sitter black holes from a geometrothermodynamic perspective","authors":"Jose M. Ladino , Carlos E. Romero-Figueroa , Hernando Quevedo","doi":"10.1016/j.nuclphysb.2024.116734","DOIUrl":"10.1016/j.nuclphysb.2024.116734","url":null,"abstract":"<div><div>We study the thermodynamic properties of the Reissner-Nordström black hole with cosmological constant, expressed in terms of the curvature radius, using the approach of shadow thermodynamics and the formalism of geometrothermodynamics. We derive explicit expressions for the shadow radius in terms of the horizon, photon sphere, and observer radii. The phase transition structure turns out to strongly depend on the value of the curvature radius, including configurations with zero, one, or two phase transitions. We also analyze the black hole's microscopic structure and find differences between the approaches of thermodynamic geometry and geometrothermodynamics, which are due to the presence of the curvature radius. We impose the important condition that the black hole is a quasi-homogeneous thermodynamic system to guarantee the consistency of the geometrothermodynamic approach.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1009 ","pages":"Article 116734"},"PeriodicalIF":2.5,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-06DOI: 10.1016/j.nuclphysb.2024.116733
Filippo Caleca , Ettore Remiddi
We evaluate the maxcut of the two loops sunrise amplitude with three different masses by direct use of the loop momenta in the Minkoskean (as opposed to the usual Euclidean) continuous dimension regularisation, obtaining in that way six related but different functions expressed in the form of one dimensional finite integrals. We then consider the 4th order homogeneous equation valid for the maxcut, and show that for arbitrary dimension d the six functions do satisfy the equation separately. We further discuss the cases, verifying that only four of them are linearly independent. The equal mass limit is also shortly considered.
{"title":"The maxcut of the sunrise with different masses in the continuous Minkoskean dimensional regularisation","authors":"Filippo Caleca , Ettore Remiddi","doi":"10.1016/j.nuclphysb.2024.116733","DOIUrl":"10.1016/j.nuclphysb.2024.116733","url":null,"abstract":"<div><div>We evaluate the <em>maxcut</em> of the two loops sunrise amplitude with three different masses by direct use of the loop momenta in the <em>Minkoskean</em> (as opposed to the usual <em>Euclidean</em>) continuous dimension regularisation, obtaining in that way six related but different functions expressed in the form of one dimensional finite integrals. We then consider the 4th order homogeneous equation valid for the maxcut, and show that for arbitrary dimension <em>d</em> the six functions do satisfy the equation separately. We further discuss the <span><math><mi>d</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></math></span> cases, verifying that only four of them are linearly independent. The equal mass limit is also shortly considered.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1009 ","pages":"Article 116733"},"PeriodicalIF":2.5,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-05DOI: 10.1016/j.nuclphysb.2024.116732
Yubo Ma , Songtao Zheng , Huaifan Li , Bangquan Li
In the theory of gravity, the spontaneous breaking of Lorentz symmetry due to the non-minimal coupling between the Kalb-Ramond field and Einstein gravity results in the existence of exactly static and spherically symmetric black hole solutions related to the Lorentz violating parameter. Based on the consideration of the interaction between the black hole and cosmological horizons, this paper studies the thermodynamic properties of Kalb-Ramond-de Sitter (KR-dS) spacetime. The Smarr relation expressed by equivalent thermodynamic quantities is found, and it is proved that the equivalent thermodynamic quantities of the KR-dS spacetime satisfy the universal Euler's theorem. It is discovered that the heat capacity of the KR-dS spacetime with respect to the ratio of the two horizons and the variation curve of the heat capacity with effective temperature possess the characteristics of Schottky specific heat. Moreover, the black hole and the cosmological horizon in the equivalent thermodynamic system are regarded as two different energy levels, and the heat capacity of the KR-dS spacetime is discussed using the general form given by the ordinary two-level system. It is found that the heat capacity of KR-dS spacetime described by equivalent thermodynamic quantities not only conforms to the characteristics of Schottky specific heat but also is consistent with the heat capacity of the ordinary two-level system. This result reflects that when the cosmological constant and the charged carried in the KR-dS spacetime remain unchanged, the heat capacity of the system can be represented by a universal two-level system. By comparing the maximum value of the heat capacity curves, the number of microscopic particles between the two horizons can be estimated, which reflects the quantum properties of the KR-dS spacetime. These studies will open a new perspective to probe the thermodynamics of black holes.
{"title":"Schottky anomaly of the Kalb-Ramond-de Sitter spacetime","authors":"Yubo Ma , Songtao Zheng , Huaifan Li , Bangquan Li","doi":"10.1016/j.nuclphysb.2024.116732","DOIUrl":"10.1016/j.nuclphysb.2024.116732","url":null,"abstract":"<div><div>In the theory of gravity, the spontaneous breaking of Lorentz symmetry due to the non-minimal coupling between the Kalb-Ramond field and Einstein gravity results in the existence of exactly static and spherically symmetric black hole solutions related to the Lorentz violating parameter. Based on the consideration of the interaction between the black hole and cosmological horizons, this paper studies the thermodynamic properties of Kalb-Ramond-de Sitter (KR-dS) spacetime. The Smarr relation expressed by equivalent thermodynamic quantities is found, and it is proved that the equivalent thermodynamic quantities of the KR-dS spacetime satisfy the universal Euler's theorem. It is discovered that the heat capacity of the KR-dS spacetime with respect to the ratio of the two horizons and the variation curve of the heat capacity with effective temperature possess the characteristics of Schottky specific heat. Moreover, the black hole and the cosmological horizon in the equivalent thermodynamic system are regarded as two different energy levels, and the heat capacity of the KR-dS spacetime is discussed using the general form given by the ordinary two-level system. It is found that the heat capacity of KR-dS spacetime described by equivalent thermodynamic quantities not only conforms to the characteristics of Schottky specific heat but also is consistent with the heat capacity of the ordinary two-level system. This result reflects that when the cosmological constant and the charged carried in the KR-dS spacetime remain unchanged, the heat capacity of the system can be represented by a universal two-level system. By comparing the maximum value of the heat capacity curves, the number of microscopic particles between the two horizons can be estimated, which reflects the quantum properties of the KR-dS spacetime. These studies will open a new perspective to probe the thermodynamics of black holes.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1009 ","pages":"Article 116732"},"PeriodicalIF":2.5,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-31DOI: 10.1016/j.nuclphysb.2024.116729
M.M. Balbino, I.P. de Freitas, R.G. Rana, F. Toppan
<div><div>Given an associative ring of <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>-graded operators, the number of inequivalent brackets of Lie-type which are compatible with the grading and satisfy graded Jacobi identities is <span><math><msub><mrow><mi>b</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><mi>n</mi><mo>+</mo><mo>⌊</mo><mi>n</mi><mo>/</mo><mn>2</mn><mo>⌋</mo><mo>+</mo><mn>1</mn></math></span>. This follows from the Rittenberg-Wyler and Scheunert analysis of “color” Lie (super)algebras which is revisited here in terms of Boolean logic gates.</div><div>The inequivalent brackets, recovered from <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mo>×</mo><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mo>→</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> mappings, are defined by consistent sets of commutators/anticommutators describing particles accommodated into an <em>n</em>-bit parastatistics (ordinary bosons/fermions correspond to 1 bit). Depending on the given graded Lie (super)algebra, its graded sectors can fall into different classes of equivalence expressing different types of particles (bosons, parabosons, fermions, parafermions). As a consequence, the assignment of certain “marked” operators to a given graded sector is a further mechanism to induce inequivalent graded Lie (super)algebras (the basic examples of quaternions, split-quaternions and biquaternions illustrate these features).</div><div>As a first application we construct <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup></math></span> and <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></msubsup></math></span>-graded quantum Hamiltonians which respectively admit <span><math><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>4</mn></math></span> and <span><math><msub><mrow><mi>b</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>=</mo><mn>5</mn></math></span> inequivalent multiparticle quantizations (the inequivalent parastatistics are discriminated by measuring the eigenvalues of certain observables in some given states). The extension to <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>-graded quantum Hamiltonians for <span><math><mi>n</mi><mo>></mo><mn>3</mn></math></span> is immediate.</div><div>As a main physical application we prove that the <span><math><mi>N</mi></math></span>-extended, one-dimensional supersymmetric and superconformal quantum mechanics, for <span><math><mi>N</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>8</mn></math></span>, are respectively described by <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>
{"title":"Inequivalent Z2n-graded brackets, n-bit parastatistics and statistical transmutations of supersymmetric quantum mechanics","authors":"M.M. Balbino, I.P. de Freitas, R.G. Rana, F. Toppan","doi":"10.1016/j.nuclphysb.2024.116729","DOIUrl":"10.1016/j.nuclphysb.2024.116729","url":null,"abstract":"<div><div>Given an associative ring of <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>-graded operators, the number of inequivalent brackets of Lie-type which are compatible with the grading and satisfy graded Jacobi identities is <span><math><msub><mrow><mi>b</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><mi>n</mi><mo>+</mo><mo>⌊</mo><mi>n</mi><mo>/</mo><mn>2</mn><mo>⌋</mo><mo>+</mo><mn>1</mn></math></span>. This follows from the Rittenberg-Wyler and Scheunert analysis of “color” Lie (super)algebras which is revisited here in terms of Boolean logic gates.</div><div>The inequivalent brackets, recovered from <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mo>×</mo><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mo>→</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> mappings, are defined by consistent sets of commutators/anticommutators describing particles accommodated into an <em>n</em>-bit parastatistics (ordinary bosons/fermions correspond to 1 bit). Depending on the given graded Lie (super)algebra, its graded sectors can fall into different classes of equivalence expressing different types of particles (bosons, parabosons, fermions, parafermions). As a consequence, the assignment of certain “marked” operators to a given graded sector is a further mechanism to induce inequivalent graded Lie (super)algebras (the basic examples of quaternions, split-quaternions and biquaternions illustrate these features).</div><div>As a first application we construct <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup></math></span> and <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></msubsup></math></span>-graded quantum Hamiltonians which respectively admit <span><math><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>4</mn></math></span> and <span><math><msub><mrow><mi>b</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>=</mo><mn>5</mn></math></span> inequivalent multiparticle quantizations (the inequivalent parastatistics are discriminated by measuring the eigenvalues of certain observables in some given states). The extension to <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>-graded quantum Hamiltonians for <span><math><mi>n</mi><mo>></mo><mn>3</mn></math></span> is immediate.</div><div>As a main physical application we prove that the <span><math><mi>N</mi></math></span>-extended, one-dimensional supersymmetric and superconformal quantum mechanics, for <span><math><mi>N</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>8</mn></math></span>, are respectively described by <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1009 ","pages":"Article 116729"},"PeriodicalIF":2.5,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-31DOI: 10.1016/j.nuclphysb.2024.116731
Amihay Hanany, Rudolph Kalveks, Guhesh Kumaran
We develop the diagrammatic technique of quiver subtraction to facilitate the identification and evaluation of the hyper-Kähler quotient (HKQ) of the Coulomb branch of a 3d unitary quiver theory. The target quivers are drawn from a wide range of theories, typically classified as “good” or “ugly”, which satisfy identified selection criteria. Our subtraction procedure uses quotient quivers that are “bad”, differing thereby from quiver subtractions based on Kraft-Procesi transitions. The simple diagrammatic procedure identifies one or more resultant quivers, the union of whose Coulomb branches corresponds to the desired HKQ. Examples include quivers whose Coulomb branches are moduli spaces of free fields, closures of nilpotent orbits of classical and exceptional type, and slices in the affine Grassmanian. We calculate the Hilbert Series and Highest Weight Generating functions for HKQ examples of low rank. For certain families of quivers, we are able to conjecture HWGs for arbitrary rank. We examine the commutation relations between quotient quiver subtraction and other diagrammatic techniques, such as Kraft-Procesi transitions, quiver folding, and discrete quotients.
{"title":"Quotient quiver subtraction","authors":"Amihay Hanany, Rudolph Kalveks, Guhesh Kumaran","doi":"10.1016/j.nuclphysb.2024.116731","DOIUrl":"10.1016/j.nuclphysb.2024.116731","url":null,"abstract":"<div><div>We develop the diagrammatic technique of quiver subtraction to facilitate the identification and evaluation of the <span><math><mrow><mi>SU</mi></mrow><mo>(</mo><mi>n</mi><mo>)</mo></math></span> hyper-Kähler quotient (HKQ) of the Coulomb branch of a 3<em>d</em> <span><math><mi>N</mi><mo>=</mo><mn>4</mn></math></span> unitary quiver theory. The target quivers are drawn from a wide range of theories, typically classified as “good” or “ugly”, which satisfy identified selection criteria. Our subtraction procedure uses quotient quivers that are “bad”, differing thereby from quiver subtractions based on Kraft-Procesi transitions. The simple diagrammatic procedure identifies one or more resultant quivers, the union of whose Coulomb branches corresponds to the desired HKQ. Examples include quivers whose Coulomb branches are moduli spaces of free fields, closures of nilpotent orbits of classical and exceptional type, and slices in the affine Grassmanian. We calculate the Hilbert Series and Highest Weight Generating functions for HKQ examples of low rank. For certain families of quivers, we are able to conjecture HWGs for arbitrary rank. We examine the commutation relations between quotient quiver subtraction and other diagrammatic techniques, such as Kraft-Procesi transitions, quiver folding, and discrete quotients.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1009 ","pages":"Article 116731"},"PeriodicalIF":2.5,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-29DOI: 10.1016/j.nuclphysb.2024.116724
Sayani Maity , Prabir Rudra
In this paper, we have studied the effects of holographic dark energy on the evolution of gravitational waves. The background evolution of gravitational waves in a flat FRW universe is considered and studied in the presence of various holographic dark energy models. The perturbation equations governing the evolution of the gravitational waves have been constructed and solutions are obtained. These solutions are studied in detail to get a proper understanding of the characteristics of the gravitational waves in the presence of holographic dark energy. The work can be a significant tool in studying different dark energy models comparatively using the features of the gravitational wave evolution.
{"title":"Gravitational waves driven by holographic dark energy","authors":"Sayani Maity , Prabir Rudra","doi":"10.1016/j.nuclphysb.2024.116724","DOIUrl":"10.1016/j.nuclphysb.2024.116724","url":null,"abstract":"<div><div>In this paper, we have studied the effects of holographic dark energy on the evolution of gravitational waves. The background evolution of gravitational waves in a flat FRW universe is considered and studied in the presence of various holographic dark energy models. The perturbation equations governing the evolution of the gravitational waves have been constructed and solutions are obtained. These solutions are studied in detail to get a proper understanding of the characteristics of the gravitational waves in the presence of holographic dark energy. The work can be a significant tool in studying different dark energy models comparatively using the features of the gravitational wave evolution.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1009 ","pages":"Article 116724"},"PeriodicalIF":2.5,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142561389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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