Pub Date : 2025-01-01DOI: 10.1016/j.nuclphysb.2024.116774
Mir Faizal , Arshid Shabir , Aatif Kaisar Khan
The observation that spacetime and quantum fields on it have to be dynamically produced in any theory of quantum gravity implies that quantum gravity should be defined on the configuration space of fields rather than spacetime. Such a theory is described on the configuration space of fields rather than spacetime, which is a third quantized theory. So, both string theory and group field theory are third-quantized theories. Thus, using axioms of string field theory, we motivate similar axioms for group field theory. Then, using the structure of these axioms for string field theory and group field theory, we identify general features of axioms for any such third quantized theory of quantum gravity. Thus, we show that such third-quantized theories of quantum gravity can be formulated as formal axiomatic systems. We then analyze the consequences of Gödel theorems on such third quantized theories. We thus address problems of consistency and completeness of any third quantized theories of quantum gravity.
{"title":"Consequences of Gödel theorems on third quantized theories like string field theory and group field theory","authors":"Mir Faizal , Arshid Shabir , Aatif Kaisar Khan","doi":"10.1016/j.nuclphysb.2024.116774","DOIUrl":"10.1016/j.nuclphysb.2024.116774","url":null,"abstract":"<div><div>The observation that spacetime and quantum fields on it have to be dynamically produced in any theory of quantum gravity implies that quantum gravity should be defined on the configuration space of fields rather than spacetime. Such a theory is described on the configuration space of fields rather than spacetime, which is a third quantized theory. So, both string theory and group field theory are third-quantized theories. Thus, using axioms of string field theory, we motivate similar axioms for group field theory. Then, using the structure of these axioms for string field theory and group field theory, we identify general features of axioms for any such third quantized theory of quantum gravity. Thus, we show that such third-quantized theories of quantum gravity can be formulated as formal axiomatic systems. We then analyze the consequences of Gödel theorems on such third quantized theories. We thus address problems of consistency and completeness of any third quantized theories of quantum gravity.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1010 ","pages":"Article 116774"},"PeriodicalIF":2.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143102209","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 : 2025-01-01DOI: 10.1016/j.nuclphysb.2024.116757
Dmitry Melnikov
We use the topological quantum field theory description of states in Chern-Simons theory to discuss the relation between spacetime connectivity and entanglement, exploring the paradigm entanglement=topology. We define a special class of states in Chern-Simons with properties similar to those of holographic states. While the holographic states are dual to classical geometries, these connectome states represent classical topologies, which satisfy a discrete analog of the Ryu-Takayanagi formula and characteristic inequalities for the entanglement entropy. Generic states are linear combinations of connectomes, and the theory also has nonperturbative states which are global spacetime defects formed by a large number of quantum fluctuations. Topological presentation of quantum states and emergence of topology from entanglement may be useful for building a generalization to geometry, that is quantum gravity. Thinking of further quantum gravity comparisons we discuss replica wormholes and conclude that similar objects exist beyond gravitational theories. The topological theory perspective suggests that the sum over all wormholes is always factorizable, even though the individual ones might not be.
{"title":"Connectomes as holographic states","authors":"Dmitry Melnikov","doi":"10.1016/j.nuclphysb.2024.116757","DOIUrl":"10.1016/j.nuclphysb.2024.116757","url":null,"abstract":"<div><div>We use the topological quantum field theory description of states in Chern-Simons theory to discuss the relation between spacetime connectivity and entanglement, exploring the paradigm entanglement=topology. We define a special class of states in Chern-Simons with properties similar to those of holographic states. While the holographic states are dual to classical geometries, these connectome states represent classical topologies, which satisfy a discrete analog of the Ryu-Takayanagi formula and characteristic inequalities for the entanglement entropy. Generic states are linear combinations of connectomes, and the theory also has nonperturbative states which are global spacetime defects formed by a large number of quantum fluctuations. Topological presentation of quantum states and emergence of topology from entanglement may be useful for building a generalization to geometry, that is quantum gravity. Thinking of further quantum gravity comparisons we discuss replica wormholes and conclude that similar objects exist beyond gravitational theories. The topological theory perspective suggests that the sum over all wormholes is always factorizable, even though the individual ones might not be.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1010 ","pages":"Article 116757"},"PeriodicalIF":2.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143102118","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 : 2025-01-01DOI: 10.1016/j.nuclphysb.2024.116772
Bao-Ping Dong , Jun-Wang Lu , Ya-Bo Wu , Cheng-Yuan Zhang , Juan-Juan Luo , Yu Tang , Hui Zhu
At the probe level, we investigate the holographic p-wave conductor/superconductor phase transition by both numerical and analytical methods. Especially, due to the nonlinear axion correction, the translational symmetry in superconductor is broken spontaneously. We then study the effects of the axion correction (or disorder) and the mass of vector field on the superconductor phase transition. Concretely, as the disorder parameter and the scaling dimension of vector operator increase, the critical temperature decreases and the stable value of condensate at the low temperature as well as the energy gap increase, which suggests that the larger mass of vector field and the disorder correction inhibit the phase transition, and increase the strength of interaction in superconductor. Near the critical point, the system always undergoes a second-order phase transition, which is independent of the disorder strength and the mass of vector field. According to the behaviors of grand potential and conductivity, the hairy state is verified to be thermodynamical favored and indeed superconducting state. Meanwhile, the analytical results uphold the numerical ones in terms of the critical behavior of condensate.
{"title":"Holographic p-wave superconductor with spontaneously broken translation","authors":"Bao-Ping Dong , Jun-Wang Lu , Ya-Bo Wu , Cheng-Yuan Zhang , Juan-Juan Luo , Yu Tang , Hui Zhu","doi":"10.1016/j.nuclphysb.2024.116772","DOIUrl":"10.1016/j.nuclphysb.2024.116772","url":null,"abstract":"<div><div>At the probe level, we investigate the holographic <em>p</em>-wave conductor/superconductor phase transition by both numerical and analytical methods. Especially, due to the nonlinear axion correction, the translational symmetry in superconductor is broken spontaneously. We then study the effects of the axion correction (or disorder) and the mass of vector field on the superconductor phase transition. Concretely, as the disorder parameter and the scaling dimension of vector operator increase, the critical temperature decreases and the stable value of condensate at the low temperature as well as the energy gap increase, which suggests that the larger mass of vector field and the disorder correction inhibit the phase transition, and increase the strength of interaction in superconductor. Near the critical point, the system always undergoes a second-order phase transition, which is independent of the disorder strength and the mass of vector field. According to the behaviors of grand potential and conductivity, the hairy state is verified to be thermodynamical favored and indeed superconducting state. Meanwhile, the analytical results uphold the numerical ones in terms of the critical behavior of condensate.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1010 ","pages":"Article 116772"},"PeriodicalIF":2.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143101651","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 : 2025-01-01DOI: 10.1016/j.nuclphysb.2024.116762
Hao-Cheng Zhang , Xiangdong Ji
We examine convergence properties of reconstructing the generalized parton distributions (GPDs) through the universal moment parameterization (GUMP). We provide a heuristic explanation for the connection between the formal summation/expansion and the Mellin-Barnes integral in the literature, and specify the exact convergence condition. We derive an asymptotic condition on the conformal moments of GPDs to satisfy the boundary condition at and subsequently develop an approximate formula for GPDs when . Since experimental observables constraining GPDs can be expressed in terms of double or even triple summations involving their moments, scale evolution factors, and Wilson coefficients, etc., we propose a method to handle the ordering of the multiple summations and convert them into multiple Mellin-Barnes integrals via analytical continuations of integer summation indices.
{"title":"On convergence properties of GPD expansion through Mellin/conformal moments and orthogonal polynomials","authors":"Hao-Cheng Zhang , Xiangdong Ji","doi":"10.1016/j.nuclphysb.2024.116762","DOIUrl":"10.1016/j.nuclphysb.2024.116762","url":null,"abstract":"<div><div>We examine convergence properties of reconstructing the generalized parton distributions (GPDs) through the universal moment parameterization (GUMP). We provide a heuristic explanation for the connection between the formal summation/expansion and the Mellin-Barnes integral in the literature, and specify the exact convergence condition. We derive an asymptotic condition on the conformal moments of GPDs to satisfy the boundary condition at <span><math><mi>x</mi><mo>=</mo><mn>1</mn></math></span> and subsequently develop an approximate formula for GPDs when <span><math><mi>x</mi><mo>></mo><mi>ξ</mi></math></span>. Since experimental observables constraining GPDs can be expressed in terms of double or even triple summations involving their moments, scale evolution factors, and Wilson coefficients, etc., we propose a method to handle the ordering of the multiple summations and convert them into multiple Mellin-Barnes integrals via analytical continuations of integer summation indices.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1010 ","pages":"Article 116762"},"PeriodicalIF":2.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143101773","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 : 2025-01-01DOI: 10.1016/j.nuclphysb.2024.116763
Chao-Shang Huang
The two Majorana CP-violating phases can not be determined by experiments on neutrino oscillations. It is difficult even almost impossible to measure two Majorana CP-violating phases since they are only sensitive to lepton-number-violating processes. One must take some assumption on the structure of neutrino mass matrix and their flavor mixing mechanism hidden behind in phenomenological models in order to determine Majorana CP-violating phases. Two models on the symmetry of the neutrino mass matrix are proposed in this paper. The Majorana CP-violating phases and the effective Majorana neutrino mass are computed in the two models. Using data in experiments on neutrino oscillations and using the limit of the absolute neutrino mass scale which is from cosmological observations, the numerical values of the Majorana CP-violating phases and the effective Majorana neutrino mass are obtained.
{"title":"Majorana CP violating phases","authors":"Chao-Shang Huang","doi":"10.1016/j.nuclphysb.2024.116763","DOIUrl":"10.1016/j.nuclphysb.2024.116763","url":null,"abstract":"<div><div>The two Majorana CP-violating phases can not be determined by experiments on neutrino oscillations. It is difficult even almost impossible to measure two Majorana CP-violating phases since they are only sensitive to lepton-number-violating processes. One must take some assumption on the structure of neutrino mass matrix and their flavor mixing mechanism hidden behind in phenomenological models in order to determine Majorana CP-violating phases. Two models on the symmetry of the neutrino mass matrix are proposed in this paper. The Majorana CP-violating phases and the effective Majorana neutrino mass <span><math><msub><mrow><mi>m</mi></mrow><mrow><mi>e</mi><mi>e</mi></mrow></msub></math></span> are computed in the two models. Using data in experiments on neutrino oscillations and using the limit of the absolute neutrino mass scale which is from cosmological observations, the numerical values of the Majorana CP-violating phases and the effective Majorana neutrino mass <span><math><msub><mrow><mi>m</mi></mrow><mrow><mi>e</mi><mi>e</mi></mrow></msub></math></span> are obtained.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1010 ","pages":"Article 116763"},"PeriodicalIF":2.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143101776","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 : 2025-01-01DOI: 10.1016/j.nuclphysb.2024.116771
Anna Pachoł
Modifications in quantum mechanical phase space lead to changes in the Heisenberg uncertainty principle, which can result in the Generalized Uncertainty Principle (GUP) or the Extended Uncertainty Principle (EUP), introducing quantum gravitational effects at small and large distances, respectively. A combination of GUP and EUP, the Generalized Extended Uncertainty Principle (GEUP or EGUP), further generalizes these modifications by incorporating noncommutativity in both coordinates and momenta. This paper examines the impact of GEUP on the analogue of the Liouville theorem in statistical physics and density of states within the classical limit of non-relativistic quantum mechanics framework. We find a weighted phase space volume element, invariant under the infinitesimal time evolution, in the cases of Snyder-de Sitter and Yang models, presenting how GEUP alters the density of states, potentially affecting physical (thermodynamical) properties. Special cases, obtained in certain limits from the above models are discussed. New higher order types of GEUP and EUP are also proposed.
{"title":"Generalized Extended Uncertainty Principles, Liouville theorem and density of states: Snyder-de Sitter and Yang models","authors":"Anna Pachoł","doi":"10.1016/j.nuclphysb.2024.116771","DOIUrl":"10.1016/j.nuclphysb.2024.116771","url":null,"abstract":"<div><div>Modifications in quantum mechanical phase space lead to changes in the Heisenberg uncertainty principle, which can result in the Generalized Uncertainty Principle (GUP) or the Extended Uncertainty Principle (EUP), introducing quantum gravitational effects at small and large distances, respectively. A combination of GUP and EUP, the Generalized Extended Uncertainty Principle (GEUP or EGUP), further generalizes these modifications by incorporating noncommutativity in both coordinates and momenta. This paper examines the impact of GEUP on the analogue of the Liouville theorem in statistical physics and density of states within the classical limit of non-relativistic quantum mechanics framework. We find a weighted phase space volume element, invariant under the infinitesimal time evolution, in the cases of Snyder-de Sitter and Yang models, presenting how GEUP alters the density of states, potentially affecting physical (thermodynamical) properties. Special cases, obtained in certain limits from the above models are discussed. New higher order types of GEUP and EUP are also proposed.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1010 ","pages":"Article 116771"},"PeriodicalIF":2.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143102115","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 : 2025-01-01DOI: 10.1016/j.nuclphysb.2024.116779
E. Sanderson , R.L. Maitra , A.J. Liberatore
Using properties of diffusion according to a quantum heat kernel constructed as an expectation over classical heat kernels on , we probe the non-manifold-like nature of quantized space in a model of (1+1)-dimensional quantum gravity. By computing the mean squared displacement of a diffusing particle, we find that diffusion is anomalous, behaving similarly to that on a porous substrate, network, or fractal over short distances. The walk dimension of the path for a particle diffusing in quantized space is calculated to have an infimum of 4, rising to arbitrarily large values depending on a parameter labeling the choice of factor ordering in the quantum Hamiltonian for our model and figuring in the asymptotic behavior of the wavefunction used to construct the quantum heat kernel. Additionally, we derive an expansion for return probability of a diffusing particle, whose modifications from the classical power-series form depend on the factor-ordering parameter.
{"title":"Anomalous diffusion and factor ordering in (1+1)-dimensional Lorentzian quantum gravity","authors":"E. Sanderson , R.L. Maitra , A.J. Liberatore","doi":"10.1016/j.nuclphysb.2024.116779","DOIUrl":"10.1016/j.nuclphysb.2024.116779","url":null,"abstract":"<div><div>Using properties of diffusion according to a quantum heat kernel constructed as an expectation over classical heat kernels on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>, we probe the non-manifold-like nature of quantized space in a model of (1+1)-dimensional quantum gravity. By computing the mean squared displacement of a diffusing particle, we find that diffusion is anomalous, behaving similarly to that on a porous substrate, network, or fractal over short distances. The walk dimension of the path for a particle diffusing in quantized space is calculated to have an infimum of 4, rising to arbitrarily large values depending on a parameter labeling the choice of factor ordering in the quantum Hamiltonian for our model and figuring in the asymptotic behavior of the wavefunction used to construct the quantum heat kernel. Additionally, we derive an expansion for return probability of a diffusing particle, whose modifications from the classical power-series form depend on the factor-ordering parameter.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1010 ","pages":"Article 116779"},"PeriodicalIF":2.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143102116","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 : 2025-01-01DOI: 10.1016/j.nuclphysb.2024.116760
Dibakar Roychowdhury
We build up the notion of metallic holography for SCFTs in four dimensions, in the presence of a finite chemical potential. We compute two point correlation functions and study their properties in the regime of low frequency and low momentum. The color sector reveals gapless excitations, one of which propagates with a finite phase velocity while the other mode attenuates through scattering. The flavour sector, on the other hand, reveals spectrum that contains quasiparticle excitations which propagate with a definite phase velocity together with modes that propagate with a finite group velocity which quantum attenuates quite similar in spirit as that of Landau's zero sound modes. We also compute associated AC conductivities, which exhibit different characteristics for different (color and flavour) sectors of SCFTs.
{"title":"Holographic zero sound for N=2 SCFTs in 4d","authors":"Dibakar Roychowdhury","doi":"10.1016/j.nuclphysb.2024.116760","DOIUrl":"10.1016/j.nuclphysb.2024.116760","url":null,"abstract":"<div><div>We build up the notion of metallic holography for <span><math><mi>N</mi><mo>=</mo><mn>2</mn></math></span> SCFTs in four dimensions, in the presence of a finite <span><math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span> chemical potential. We compute two point correlation functions and study their properties in the regime of low frequency and low momentum. The color sector reveals gapless excitations, one of which propagates with a finite phase velocity while the other mode attenuates through scattering. The flavour sector, on the other hand, reveals spectrum that contains quasiparticle excitations which propagate with a definite phase velocity together with modes that propagate with a finite group velocity which quantum attenuates quite similar in spirit as that of Landau's zero sound modes. We also compute associated AC conductivities, which exhibit different characteristics for different (color and flavour) sectors of <span><math><mi>N</mi><mo>=</mo><mn>2</mn></math></span> SCFTs.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1010 ","pages":"Article 116760"},"PeriodicalIF":2.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143102210","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 : 2025-01-01DOI: 10.1016/j.nuclphysb.2024.116782
Nikos Irges, Leonidas Karageorgos
We revisit the construction of the renormalized trace Θ of the Energy-Momentum tensor in the four-dimensional theory, using dimensional regularization in dimensions. We first construct several basic correlators such as , to order and from these the correlators and with the basis of dimension d operators. We then match the limit of their expressions on the Wilson-Fisher fixed point to the corresponding expressions obtained in Conformal Field Theory. Then, using the 3-point function , we construct the operator Θ as a certain linear combination of the basis operators, using the requirements that Θ should vanish on the fixed point and that it should have zero anomalous dimension. Finally, we compute the 2-point function and we show that it obeys an eigenvalue equation that gives additional information about the internal structure of the Energy-Momentum tensor operator to what is already contained in its Callan-Symanzik equation.
{"title":"Energy-Momentum tensor correlators in ϕ4 theory I: The spin-zero sector","authors":"Nikos Irges, Leonidas Karageorgos","doi":"10.1016/j.nuclphysb.2024.116782","DOIUrl":"10.1016/j.nuclphysb.2024.116782","url":null,"abstract":"<div><div>We revisit the construction of the renormalized trace Θ of the Energy-Momentum tensor in the four-dimensional <span><math><mi>λ</mi><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> theory, using dimensional regularization in <span><math><mi>d</mi><mo>=</mo><mn>4</mn><mo>−</mo><mi>ε</mi></math></span> dimensions. We first construct several basic correlators such as <span><math><mo>〈</mo><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>ϕ</mi><mi>ϕ</mi><mo>〉</mo></math></span>, <span><math><mo>〈</mo><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>4</mn></mrow></msup><mi>ϕ</mi><mi>ϕ</mi><mo>〉</mo></math></span> to order <span><math><msup><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and from these the correlators <span><math><mo>〈</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>I</mi></mrow></msub><mi>ϕ</mi><mi>ϕ</mi><mo>〉</mo></math></span> and <span><math><mo>〈</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>I</mi></mrow></msub><msub><mrow><mi>K</mi></mrow><mrow><mi>J</mi></mrow></msub><mo>〉</mo></math></span> with <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>I</mi></mrow></msub></math></span> the basis of dimension <em>d</em> operators. We then match the limit of their expressions on the Wilson-Fisher fixed point to the corresponding expressions obtained in Conformal Field Theory. Then, using the 3-point function <span><math><mo>〈</mo><mi>Θ</mi><mi>ϕ</mi><mi>ϕ</mi><mo>〉</mo></math></span>, we construct the operator Θ as a certain linear combination of the basis operators, using the requirements that Θ should vanish on the fixed point and that it should have zero anomalous dimension. Finally, we compute the 2-point function <span><math><mo>〈</mo><mi>Θ</mi><mi>Θ</mi><mo>〉</mo></math></span> and we show that it obeys an eigenvalue equation that gives additional information about the internal structure of the Energy-Momentum tensor operator to what is already contained in its Callan-Symanzik equation.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1010 ","pages":"Article 116782"},"PeriodicalIF":2.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143102159","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 : 2025-01-01DOI: 10.1016/j.nuclphysb.2024.116765
H. Itoyama , R. Yoshioka
Continuing with our previous series of work, we present a case study of the critical phenomena around Argyres-Douglas singularity of susy made at realized by one-unitary matrix model. We determine the phase diagram, which is recast into LEEA of , 4d gauge theory by the 0d-4d connection. There are three distinct phases, each corresponding to an eigenvalue distribution with 0, 1, and 2 gaps. These form an entire phase diagram with a triple point. Examining the behavior of the planar free energy, we show, among other things, that the transition line between 1- and 2-gap phases ending at the triple point is the multicritical one.
{"title":"Phases and triple (multiple) point: Critical phenomena around the AD singularity","authors":"H. Itoyama , R. Yoshioka","doi":"10.1016/j.nuclphysb.2024.116765","DOIUrl":"10.1016/j.nuclphysb.2024.116765","url":null,"abstract":"<div><div>Continuing with our previous series of work, we present a case study of the critical phenomena around Argyres-Douglas singularity of <span><math><mi>N</mi><mo>=</mo><mn>2</mn></math></span> susy made at <span><math><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>)</mo><mo>,</mo><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></math></span> realized by one-unitary matrix model. We determine the phase diagram, which is recast into LEEA of <span><math><mi>N</mi><mo>=</mo><mn>2</mn></math></span>, 4d gauge theory by the 0d-4d connection. There are three distinct phases, each corresponding to an eigenvalue distribution with 0, 1, and 2 gaps. These form an entire phase diagram with a triple point. Examining the behavior of the planar free energy, we show, among other things, that the transition line between 1- and 2-gap phases ending at the triple point is the <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span> multicritical one.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1010 ","pages":"Article 116765"},"PeriodicalIF":2.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143102114","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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