Hiroaki W H Tahara, Kazufumi Takahashi, Masato Minamitsuji, Hayato Motohashi
It has recently been pointed out that one can construct invertible conformal transformations with a parity-violating conformal factor, which can be employed to generate a novel class of parity-violating ghost-free metric theories from general relativity. We obtain exact solutions for rotating black holes in such theories by performing the conformal transformation on the Kerr solution in general relativity, which we dub conformal Kerr solutions. We explore the geodesic motion of a test particle in the conformal Kerr spacetime. While null geodesics remain the same as those in the Kerr spacetime, timelike geodesics exhibit interesting differences due to an effective external force caused by the parity-violating conformal factor.
{"title":"Exact solution for rotating black holes in parity-violating gravity","authors":"Hiroaki W H Tahara, Kazufumi Takahashi, Masato Minamitsuji, Hayato Motohashi","doi":"10.1093/ptep/ptae046","DOIUrl":"https://doi.org/10.1093/ptep/ptae046","url":null,"abstract":"It has recently been pointed out that one can construct invertible conformal transformations with a parity-violating conformal factor, which can be employed to generate a novel class of parity-violating ghost-free metric theories from general relativity. We obtain exact solutions for rotating black holes in such theories by performing the conformal transformation on the Kerr solution in general relativity, which we dub conformal Kerr solutions. We explore the geodesic motion of a test particle in the conformal Kerr spacetime. While null geodesics remain the same as those in the Kerr spacetime, timelike geodesics exhibit interesting differences due to an effective external force caused by the parity-violating conformal factor.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"18 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140598119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Motivated by the picture of partial deconfinement developed in recent years for large-N gauge theories, we propose a new way of analyzing and understanding thermal phase transition in QCD. We find nontrivial support for our proposal by analyzing the WHOT-QCD collaboration’s lattice configurations for SU(3) QCD in 3 + 1 spacetime dimensions with up, down, and strange quarks. We find that the Polyakov line (the holonomy matrix around a thermal time circle) is governed by the Haar-random distribution at low temperatures. The deviation from the Haar-random distribution at higher temperatures can be measured via the character expansion, or equivalently, via the expectation values of the Polyakov loop defined by the various nontrivial representations of SU(3). We find that the Polyakov loop corresponding to the fundamental representation and loops in the higher representation condense at different temperatures. This suggests that there are three phases, one intermediate phase existing in between the completely-confined and the completely-deconfined phases. Our identification of the intermediate phase is supported also by the condensation of instantons: by studying the instanton numbers of the WHOT-QCD configurations, we find that the instanton condensation occurs for temperature regimes corresponding to what we identify as the completely-confined and intermediate phases, whereas the instantons do not condense in the completely-deconfined phase. Our characterization of confinement based on the Haar-randomness explains why the Polyakov loop is a good observable to distinguish the confinement and the deconfinement phases in QCD despite the absence of the $mathbb {Z}_3$ center symmetry.
{"title":"A new perspective on thermal transition in QCD","authors":"Masanori Hanada, Hiroki Ohata, Hidehiko Shimada, Hiromasa Watanabe","doi":"10.1093/ptep/ptae044","DOIUrl":"https://doi.org/10.1093/ptep/ptae044","url":null,"abstract":"Motivated by the picture of partial deconfinement developed in recent years for large-N gauge theories, we propose a new way of analyzing and understanding thermal phase transition in QCD. We find nontrivial support for our proposal by analyzing the WHOT-QCD collaboration’s lattice configurations for SU(3) QCD in 3 + 1 spacetime dimensions with up, down, and strange quarks. We find that the Polyakov line (the holonomy matrix around a thermal time circle) is governed by the Haar-random distribution at low temperatures. The deviation from the Haar-random distribution at higher temperatures can be measured via the character expansion, or equivalently, via the expectation values of the Polyakov loop defined by the various nontrivial representations of SU(3). We find that the Polyakov loop corresponding to the fundamental representation and loops in the higher representation condense at different temperatures. This suggests that there are three phases, one intermediate phase existing in between the completely-confined and the completely-deconfined phases. Our identification of the intermediate phase is supported also by the condensation of instantons: by studying the instanton numbers of the WHOT-QCD configurations, we find that the instanton condensation occurs for temperature regimes corresponding to what we identify as the completely-confined and intermediate phases, whereas the instantons do not condense in the completely-deconfined phase. Our characterization of confinement based on the Haar-randomness explains why the Polyakov loop is a good observable to distinguish the confinement and the deconfinement phases in QCD despite the absence of the $mathbb {Z}_3$ center symmetry.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"56 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140598505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yeong-Bok Bae, Chan Park, Edwin J Son, Sang-Hyeon Ahn, Minjoong Jeong, Gungwon Kang, Chunglee Kim, Dong Lak Kim, Jaewan Kim, Whansun Kim Hyung Mok Lee, Yong-Ho Lee, Ronald S Norton, John J Oh, Sang Hoon Oh, Ho Jung Paik
Mid-frequency band gravitational-wave detectors will be complementary for the existing Earth-based detectors (sensitive above 10 Hz or so) and the future space-based detectors such as LISA, which will be sensitive below around 10 mHz. A ground-based superconducting omnidirectional gravitational radiation observatory (SOGRO) has recently been proposed along with several design variations for the frequency band of 0.1 to 10 Hz. For two conceptual designs of SOGRO (e.g., SOGRO and aSOGRO), we examine their multi-channel natures, sensitivities and science cases. One of the key characteristics of the SOGRO concept is its six detection channels. The response functions of each channel are calculated for all possible gravitational wave polarizations including scalar and vector modes. Combining these response functions, we also confirm the omnidirectional nature of SOGRO. Hence, even a single SOGRO detector will be able to determine the position of a source and polarizations of gravitational waves, if detected. Taking into account SOGRO’s sensitivity and technical requirements, two main targets are most plausible: gravitational waves from compact binaries and stochastic backgrounds. Based on assumptions we consider in this work, detection rates for intermediate-mass binary black holes (in the mass range of hundreds up to 105 M⊙) are expected to be 0.0065 − 8.1 yr−1. In order to detect stochastic gravitational wave background, multiple detectors are required. Two aSOGRO detector networks may be able to put limits on the stochastic background beyond the indirect limit from cosmological observations.
{"title":"A superconducting tensor detector for mid-frequency gravitational waves: its multi-channel nature and main astrophysical targets","authors":"Yeong-Bok Bae, Chan Park, Edwin J Son, Sang-Hyeon Ahn, Minjoong Jeong, Gungwon Kang, Chunglee Kim, Dong Lak Kim, Jaewan Kim, Whansun Kim Hyung Mok Lee, Yong-Ho Lee, Ronald S Norton, John J Oh, Sang Hoon Oh, Ho Jung Paik","doi":"10.1093/ptep/ptae045","DOIUrl":"https://doi.org/10.1093/ptep/ptae045","url":null,"abstract":"Mid-frequency band gravitational-wave detectors will be complementary for the existing Earth-based detectors (sensitive above 10 Hz or so) and the future space-based detectors such as LISA, which will be sensitive below around 10 mHz. A ground-based superconducting omnidirectional gravitational radiation observatory (SOGRO) has recently been proposed along with several design variations for the frequency band of 0.1 to 10 Hz. For two conceptual designs of SOGRO (e.g., SOGRO and aSOGRO), we examine their multi-channel natures, sensitivities and science cases. One of the key characteristics of the SOGRO concept is its six detection channels. The response functions of each channel are calculated for all possible gravitational wave polarizations including scalar and vector modes. Combining these response functions, we also confirm the omnidirectional nature of SOGRO. Hence, even a single SOGRO detector will be able to determine the position of a source and polarizations of gravitational waves, if detected. Taking into account SOGRO’s sensitivity and technical requirements, two main targets are most plausible: gravitational waves from compact binaries and stochastic backgrounds. Based on assumptions we consider in this work, detection rates for intermediate-mass binary black holes (in the mass range of hundreds up to 105 M⊙) are expected to be 0.0065 − 8.1 yr−1. In order to detect stochastic gravitational wave background, multiple detectors are required. Two aSOGRO detector networks may be able to put limits on the stochastic background beyond the indirect limit from cosmological observations.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"25 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140598113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S K Maurya, Abdelghani Errehymy, G Mustafa, Orhan Donmez, Kottakkaran Sooppy Nisar, Abdel-Haleem Abdel-Aty
In this study, we explore a new exact solution for a charged spherical model as well as the astrophysical implications of the torsion parameter χ1 and electric charge Q on compact stars in lower mass gaps in the $f(mathcal {T})$ gravity framework. Commencing with the field equations that describe anisotropic matter distributions, we select a well-behaved ansatz for the radial component of the metric function, along with an appropriate formulation for the electric field. The resulting model undergoes rigorous testing to ensure its qualification as a physically viable compact object within the $f(mathcal {T})$ gravity background. We extensively investigate two factors: χ1 and Q, carefully analyzing their impacts on the mass, radius, and stability of the star. Our analyses demonstrate that our models exhibit well-behaved behavior, free from singularities, and can successfully explain the existence of a wide range of observed compact objects. These objects have masses ranging from $0.85^{+0.15}_{-0.15}$ to 2.67 M⊙, with the upper value falling within the mass gap regime observed in gravitational events like GW190814. A notable finding of this study has two aspects: we observe significant effects on the maximum mass (Mmax) and the corresponding radii of these objects. Increasing values of χ1 lead to higher Mmax (approximately $2.64^{+0.13}_{-0.14}$) and smaller radii (approximately $10.40^{+0.16}_{-0.60}$), suggesting the possibility of the existence of massive neutron stars (NSs) within the system. Conversely, increasing values of Q result in a decrease in Mmax (approximately $1.70^{+0.05}_{-0.03}$) and larger radii (approximately $13.71^{+0.19}_{-0.20}$). Furthermore, an intriguing observation arises from comparing the results: for all values of χ1, non-rotating stars possess higher masses compared to slow-rotating stars, while this trend is reversed when adjusting Q.
{"title":"Charged spherical solution in torsion and matter coupling gravity and influence of torsion parameter and electric charge on compact stars in lower mass gap","authors":"S K Maurya, Abdelghani Errehymy, G Mustafa, Orhan Donmez, Kottakkaran Sooppy Nisar, Abdel-Haleem Abdel-Aty","doi":"10.1093/ptep/ptae043","DOIUrl":"https://doi.org/10.1093/ptep/ptae043","url":null,"abstract":"In this study, we explore a new exact solution for a charged spherical model as well as the astrophysical implications of the torsion parameter χ1 and electric charge Q on compact stars in lower mass gaps in the $f(mathcal {T})$ gravity framework. Commencing with the field equations that describe anisotropic matter distributions, we select a well-behaved ansatz for the radial component of the metric function, along with an appropriate formulation for the electric field. The resulting model undergoes rigorous testing to ensure its qualification as a physically viable compact object within the $f(mathcal {T})$ gravity background. We extensively investigate two factors: χ1 and Q, carefully analyzing their impacts on the mass, radius, and stability of the star. Our analyses demonstrate that our models exhibit well-behaved behavior, free from singularities, and can successfully explain the existence of a wide range of observed compact objects. These objects have masses ranging from $0.85^{+0.15}_{-0.15}$ to 2.67 M⊙, with the upper value falling within the mass gap regime observed in gravitational events like GW190814. A notable finding of this study has two aspects: we observe significant effects on the maximum mass (Mmax) and the corresponding radii of these objects. Increasing values of χ1 lead to higher Mmax (approximately $2.64^{+0.13}_{-0.14}$) and smaller radii (approximately $10.40^{+0.16}_{-0.60}$), suggesting the possibility of the existence of massive neutron stars (NSs) within the system. Conversely, increasing values of Q result in a decrease in Mmax (approximately $1.70^{+0.05}_{-0.03}$) and larger radii (approximately $13.71^{+0.19}_{-0.20}$). Furthermore, an intriguing observation arises from comparing the results: for all values of χ1, non-rotating stars possess higher masses compared to slow-rotating stars, while this trend is reversed when adjusting Q.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"129 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A non-perturbative effect in κ (renormalized string coupling) obtained from the large order behavior in the vicinity of the prototypical Argyres-Douglas critical point of su(2), Nf = 2, $0mathcal {N} =2$ susy gauge theory can be studied in the GWW unitary matrix model with the log term: the one as the work done against the barrier of the effective potential by a single eigenvalue lifted from the sea and the other as a non-perturbative function contained in the solutions of the nonlinear differential equation PII that goes beyond the asymptotic series. The leading behaviors are of the form $exp (-frac{4}{3}frac{1}{kappa } , (1, left(frac{s}{K}right)^{frac{3}{2}} ))$ respectively. We make comments on their agreement.
{"title":"Large order behavior near the AD point: the case of N = 2 , su(2), Nf = 2","authors":"Chuan-Tsung Chan, H Itoyama, R Yoshioka","doi":"10.1093/ptep/ptae034","DOIUrl":"https://doi.org/10.1093/ptep/ptae034","url":null,"abstract":"A non-perturbative effect in κ (renormalized string coupling) obtained from the large order behavior in the vicinity of the prototypical Argyres-Douglas critical point of su(2), Nf = 2, $0mathcal {N} =2$ susy gauge theory can be studied in the GWW unitary matrix model with the log term: the one as the work done against the barrier of the effective potential by a single eigenvalue lifted from the sea and the other as a non-perturbative function contained in the solutions of the nonlinear differential equation PII that goes beyond the asymptotic series. The leading behaviors are of the form $exp (-frac{4}{3}frac{1}{kappa } , (1, left(frac{s}{K}right)^{frac{3}{2}} ))$ respectively. We make comments on their agreement.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"251 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140302169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Thermal radiation is found from a moving point charge along a special, globally defined, continuous accelerated trajectory. The calculation is entirely classical (despite the appearance of ℏ) but is shown to have an immediate connection to quantum field theory via the moving mirror model. A precise recipe is given for the functional mathematical identity of the electron-mirror duality that allows one to map between (1) the classical radiation of an ordinary accelerating point charge in 3+1 Minkowski spacetime and (2) the quantum radiation of a moving mirror in 1+1 flat spacetime, for a given rectilinear trajectory.
{"title":"Thermal Larmor radiation","authors":"Evgenii Ievlev, Michael R R Good","doi":"10.1093/ptep/ptae042","DOIUrl":"https://doi.org/10.1093/ptep/ptae042","url":null,"abstract":"Thermal radiation is found from a moving point charge along a special, globally defined, continuous accelerated trajectory. The calculation is entirely classical (despite the appearance of ℏ) but is shown to have an immediate connection to quantum field theory via the moving mirror model. A precise recipe is given for the functional mathematical identity of the electron-mirror duality that allows one to map between (1) the classical radiation of an ordinary accelerating point charge in 3+1 Minkowski spacetime and (2) the quantum radiation of a moving mirror in 1+1 flat spacetime, for a given rectilinear trajectory.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"162 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the standard lattice domain-wall fermion formulation, one needs two flat domain-walls where both of the left- and right-handed massless modes appear. In this work we investigate a single domain-wall system with a nontrivial curved background. Specifically we consider a massive fermion on a three-dimensional square lattice, whose domain-wall is a two-dimensional sphere. In the free theory, we find that a single Weyl fermion is localized at the wall and it feels gravity through the induced spin connection. With a topologically nontrivial U(1) link gauge field, however, we find a zero mode with the opposite chirality localized at the center where the gauge field is singular. In the latter case, the low-energy effective theory is not chiral but vectorlike. We discuss how to circumvent this obstacle in formulating lattice chiral gauge theory in the single domain-wall fermion system.
{"title":"A lattice formulation of Weyl fermions on a single curved surface","authors":"Shoto Aoki, Hidenori Fukaya, Naoto Kan","doi":"10.1093/ptep/ptae041","DOIUrl":"https://doi.org/10.1093/ptep/ptae041","url":null,"abstract":"In the standard lattice domain-wall fermion formulation, one needs two flat domain-walls where both of the left- and right-handed massless modes appear. In this work we investigate a single domain-wall system with a nontrivial curved background. Specifically we consider a massive fermion on a three-dimensional square lattice, whose domain-wall is a two-dimensional sphere. In the free theory, we find that a single Weyl fermion is localized at the wall and it feels gravity through the induced spin connection. With a topologically nontrivial U(1) link gauge field, however, we find a zero mode with the opposite chirality localized at the center where the gauge field is singular. In the latter case, the low-energy effective theory is not chiral but vectorlike. We discuss how to circumvent this obstacle in formulating lattice chiral gauge theory in the single domain-wall fermion system.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"33 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140205664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The existence of p-form symmetry in (d + 1)-dimensional quantum field is known to always lead to the breakdown of the eigenstate thermalization hypothesis (ETH) for certain (d − p)-dimensional operators other than symmetry operators under some assumptions. The assumptions include the mixing of symmetry sectors within a given energy shell, which is rather challenging to verify because it requires information on the eigenstates in the middle of the spectrum. We reconsider this assumption from the viewpoint of projective representations to avoid this difficulty. In the case of $mathbb {Z}_N$ symmetries, we can circumvent the difficulty by considering $mathbb {Z}_Ntimes mathbb {Z}_N$-symmetric theories with nontrivial projective phases, and perturbing the Hamiltonian while preserving one of the $mathbb {Z}_N$ symmetries of our interest. We also perform numerical analyses for (1 + 1)-dimensional spin chains and the (2 + 1)-dimensional $mathbb {Z}_2$ lattice gauge theory.
{"title":"Remarks on effects of projective phase on eigenstate thermalization hypothesis","authors":"Osamu Fukushima","doi":"10.1093/ptep/ptae039","DOIUrl":"https://doi.org/10.1093/ptep/ptae039","url":null,"abstract":"The existence of p-form symmetry in (d + 1)-dimensional quantum field is known to always lead to the breakdown of the eigenstate thermalization hypothesis (ETH) for certain (d − p)-dimensional operators other than symmetry operators under some assumptions. The assumptions include the mixing of symmetry sectors within a given energy shell, which is rather challenging to verify because it requires information on the eigenstates in the middle of the spectrum. We reconsider this assumption from the viewpoint of projective representations to avoid this difficulty. In the case of $mathbb {Z}_N$ symmetries, we can circumvent the difficulty by considering $mathbb {Z}_Ntimes mathbb {Z}_N$-symmetric theories with nontrivial projective phases, and perturbing the Hamiltonian while preserving one of the $mathbb {Z}_N$ symmetries of our interest. We also perform numerical analyses for (1 + 1)-dimensional spin chains and the (2 + 1)-dimensional $mathbb {Z}_2$ lattice gauge theory.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"41 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140116656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In U(1) lattice gauge theory with compact U(1) variables, we construct the symmetry operator, i.e., the topological defect, for the axial U(1) non-invertible symmetry. This requires a lattice formulation of chiral gauge theory with an anomalous matter content and we employ the lattice formulation on the basis of the Ginsparg–Wilson relation. The invariance of the symmetry operator under the gauge transformation of the gauge field on the defect is realized, imitating the prescription by Karasik in continuum theory, by integrating the lattice Chern–Simons term on the defect over smooth lattice gauge transformations. The projection operator for allowed magnetic fluxes on the defect then emerges with lattice regularization. The resulting symmetry operator is manifestly invariant under lattice gauge transformations. In an appendix, we give another way of constructing the symmetry operator on the basis of a 3D $mathbb {Z}_N$ TQFT, the level-N BF theory on the lattice.
{"title":"Lattice realization of the axial U(1) non-invertible symmetry","authors":"Yamato Honda, Okuto Morikawa, Soma Onoda, Hiroshi Suzuki","doi":"10.1093/ptep/ptae040","DOIUrl":"https://doi.org/10.1093/ptep/ptae040","url":null,"abstract":"In U(1) lattice gauge theory with compact U(1) variables, we construct the symmetry operator, i.e., the topological defect, for the axial U(1) non-invertible symmetry. This requires a lattice formulation of chiral gauge theory with an anomalous matter content and we employ the lattice formulation on the basis of the Ginsparg–Wilson relation. The invariance of the symmetry operator under the gauge transformation of the gauge field on the defect is realized, imitating the prescription by Karasik in continuum theory, by integrating the lattice Chern–Simons term on the defect over smooth lattice gauge transformations. The projection operator for allowed magnetic fluxes on the defect then emerges with lattice regularization. The resulting symmetry operator is manifestly invariant under lattice gauge transformations. In an appendix, we give another way of constructing the symmetry operator on the basis of a 3D $mathbb {Z}_N$ TQFT, the level-N BF theory on the lattice.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"26 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we study the thermodynamic topology of a static, a charged static and a charged, rotating black hole in f(R) gravity. For charged static black holes, we work in two different ensembles: fixed charge(q) ensemble and fixed potential(φ) ensemble. For charged, rotating black hole, four different types of ensembles are considered: fixed (q, J), fixed (φ, J), fixed (q, Ω) and fixed (φ, Ω) ensemble, where J and Ω denotes the angular momentum and the angular frequency respectively. Using the generalized off-shell free energy method, where the black holes are treated as topological defects in their thermodynamic spaces, we investigate the local and global topology of these black holes via the computation of winding numbers at these defects. For static black hole we work in three model. We find that the topological charge for a static black hole is always −1 regardless of the values of the thermodynamic parameters and the choice of f(R) model. For a charged static black hole, in the fixed charge ensemble, the topological charge is found to be zero. Contrastingly, in the fixed φ ensemble, the topological charge is found to be −1. For charged static black holes, in both the ensembles, the topological charge is observed to be independent of the thermodynamic parameters. For charged, rotating black hole, in fixed (q, J) ensemble, the topological charge is found to be 1. In (φ, J) ensemble, we find the topological charge to be 1. In case of fixed (q, Ω) ensemble, the topological charge is 1 or 0 depending on the value of the scalar curvature(R). In fixed (Ω, φ) ensemble, the topological charge is −1, 0 or 1 depending on the values of R, Ω and φ. Therefore, we conclude that the thermodynamic topologies of the charged static black hole and charged rotating black hole are influenced by the choice of ensemble. In addition, the thermodynamic topology of the charged rotating black hole also depends on the thermodynamic parameters.
{"title":"Thermodynamic topology of black holes in f(R) gravity","authors":"Bidyut Hazarika, Prabwal Phukon","doi":"10.1093/ptep/ptae035","DOIUrl":"https://doi.org/10.1093/ptep/ptae035","url":null,"abstract":"In this work, we study the thermodynamic topology of a static, a charged static and a charged, rotating black hole in f(R) gravity. For charged static black holes, we work in two different ensembles: fixed charge(q) ensemble and fixed potential(φ) ensemble. For charged, rotating black hole, four different types of ensembles are considered: fixed (q, J), fixed (φ, J), fixed (q, Ω) and fixed (φ, Ω) ensemble, where J and Ω denotes the angular momentum and the angular frequency respectively. Using the generalized off-shell free energy method, where the black holes are treated as topological defects in their thermodynamic spaces, we investigate the local and global topology of these black holes via the computation of winding numbers at these defects. For static black hole we work in three model. We find that the topological charge for a static black hole is always −1 regardless of the values of the thermodynamic parameters and the choice of f(R) model. For a charged static black hole, in the fixed charge ensemble, the topological charge is found to be zero. Contrastingly, in the fixed φ ensemble, the topological charge is found to be −1. For charged static black holes, in both the ensembles, the topological charge is observed to be independent of the thermodynamic parameters. For charged, rotating black hole, in fixed (q, J) ensemble, the topological charge is found to be 1. In (φ, J) ensemble, we find the topological charge to be 1. In case of fixed (q, Ω) ensemble, the topological charge is 1 or 0 depending on the value of the scalar curvature(R). In fixed (Ω, φ) ensemble, the topological charge is −1, 0 or 1 depending on the values of R, Ω and φ. Therefore, we conclude that the thermodynamic topologies of the charged static black hole and charged rotating black hole are influenced by the choice of ensemble. In addition, the thermodynamic topology of the charged rotating black hole also depends on the thermodynamic parameters.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"12 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140054965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：