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JT gravity and the ensembles of random matrix theory JT重力与随机矩阵理论的系综
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-07-07 DOI: 10.4310/atmp.2020.v24.n6.a4
D. Stanford, E. Witten
{"title":"JT gravity and the ensembles of random matrix theory","authors":"D. Stanford, E. Witten","doi":"10.4310/atmp.2020.v24.n6.a4","DOIUrl":"https://doi.org/10.4310/atmp.2020.v24.n6.a4","url":null,"abstract":"We generalize the recently discovered relationship between JT gravity and double-scaled random matrix theory to the case that the boundary theory may have time-reversal symmetry and may have fermions with or without supersymmetry. The matching between variants of JT gravity and matrix ensembles depends on the assumed symmetries. Time-reversal symmetry in the boundary theory means that unorientable spacetimes must be considered in the bulk. In such a case, the partition function of JT gravity is still related to the volume of the moduli space of conformal structures, but this volume has a quantum correction and has to be computed using Reidemeister-Ray-Singer \"torsion.\" Presence of fermions in the boundary theory (and thus a symmetry $(-1)^F$) means that the bulk has a spin or pin structure. Supersymmetry in the boundary means that the bulk theory is associated to JT supergravity and is related to the volume of the moduli space of super Riemann surfaces rather than of ordinary Riemann surfaces. In all cases we match JT gravity or supergravity with an appropriate random matrix ensemble. All ten standard random matrix ensembles make an appearance -- the three Dyson ensembles and the seven Altland-Zirnbauer ensembles. To facilitate the analysis, we extend to the other ensembles techniques that are most familiar in the case of the original Wigner-Dyson ensemble of hermitian matrices. We also generalize Mirzakhani's recursion for the volumes of ordinary moduli space to the case of super Riemann surfaces.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88284595","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}
引用次数: 222
Heat kernel for the quantum Rabi model 量子拉比模型的热核
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-06-23 DOI: 10.4310/ATMP.2022.v26.n5.a8
Cid Reyes-Bustos, M. Wakayama
{"title":"Heat kernel for the quantum Rabi model","authors":"Cid Reyes-Bustos, M. Wakayama","doi":"10.4310/ATMP.2022.v26.n5.a8","DOIUrl":"https://doi.org/10.4310/ATMP.2022.v26.n5.a8","url":null,"abstract":"The quantum Rabi model (QRM) is widely recognized as a particularly important model in quantum optics. It is considered to be the simplest and most fundamental system describing quantum light-matter interaction. The objective of the paper is to give an analytical formula of the heat kernel of the Hamiltonian explicitly by infinite series of iterated integrals. The derivation of the formula is based on the direct evaluation of the Trotter-Kato product formula without the use of Feynman-Kac path integrals. More precisely, the infinite sum in the expression of the heat kernel arises from the reduction of the Trotter-Kato product formula into sums over the orbits of the action of the infinite symmetric group $mathfrak{S}_infty$ on the group $mathbb{Z}_2^{infty}$, and the iterated integrals are then considered as the orbital integral for each orbit. Here, the groups $ mathbb{Z}_2^{infty} $ and $mathfrak{S}_infty$ are the inductive limit of the families ${mathbb{Z}_2^n}_{ngeq0}$ and ${mathfrak{S}_n}_{ngeq0}$, respectively. In order to complete the reduction, an extensive study of harmonic (Fourier) analysis on the inductive family of abelian groups $mathbb{Z}_2^n, (n geq0)$ together with a graph theoretical investigation is crucial. To the best knowledge of the authors, this is the first explicit computation for obtaining a closed formula of the heat kernel for a non-trivial realistic interacting quantum system. The heat kernel of this model is further given by a two-by-two matrix valued function and is expressed as a direct sum of two respective heat kernels representing the parity ($mathbb{Z}_2$-symmetry) decomposition of the Hamiltonian by parity.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74792004","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}
引用次数: 6
Blowup rate control for solution of Jang’s equation and its application to Penrose inequality Jang方程解的爆破速率控制及其在Penrose不等式上的应用
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-06-20 DOI: 10.7916/d8-avnq-g588
Wenhuan Yu
{"title":"Blowup rate control for solution of Jang’s equation and its application to Penrose inequality","authors":"Wenhuan Yu","doi":"10.7916/d8-avnq-g588","DOIUrl":"https://doi.org/10.7916/d8-avnq-g588","url":null,"abstract":"We prove that the blowup term of a blowup solution of Jang's equation on an initial data set (M,g,k) near an arbitrary strictly stable MOTS $ Sigma $ is exactly $ -frac{1}{sqrt{lambda}}log tau $, where $ tau $ is the distance from $ Sigma $ and $ lambda $ is the principal eigenvalue of the MOTS stability operator of $ Sigma $. We also prove that the gradient of the solution is of order $ tau^{-1} $. Moreover, we apply these results to get a Penrose-like inequality under additional assumptions.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79056127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Heterotic/$F$-theory duality and Narasimhan–Seshadri equivalence 异质性/$F$-理论二象性与Narasimhan-Seshadri等价
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-06-17 DOI: 10.4310/atmp.2021.v25.n5.a2
H. Clemens, S. Raby
{"title":"Heterotic/$F$-theory duality and Narasimhan–Seshadri equivalence","authors":"H. Clemens, S. Raby","doi":"10.4310/atmp.2021.v25.n5.a2","DOIUrl":"https://doi.org/10.4310/atmp.2021.v25.n5.a2","url":null,"abstract":"Finding the $F$-theory dual of a Heterotic model with Wilson-line symmetry breaking presents the challenge of achieving the dual $mathbb{Z}_{2}$-action on the $F$-theory model in such a way that the $mathbb{Z}_{2}$-quotient is Calabi-Yau with an Enriques $mathrm{GUT}$ surface over which $SUleft(5right)_{gauge}$ symmetry is maintained. We propose a new way to approach this problem by taking advantage of a little-noticed choice in the application of Narasimhan-Seshadri equivalence between real $E_{8}$-bundles with Yang-Mills connection and their associated complex holomorphic $E_{8}^{mathbb{C}}$-bundles, namely the one given by the real outer automorphism of $E_{8}^{mathbb{C}}$ by complex conjugation. The triviality of the restriction on the compact real form $E_{8}$ allows one to introduce it into the $mathbb{Z}_{2}$-action, thereby restoring $E_{8}$- and hence $SUleft(5right)_{gauge}$ -symmetry on which the Wilson line can be wrapped.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90401372","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}
引用次数: 6
Anomaly cancellation in the topological string 拓扑字符串中的异常消除
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-05-22 DOI: 10.4310/atmp.2020.v24.n7.a2
K. Costello, Si Li
{"title":"Anomaly cancellation in the topological string","authors":"K. Costello, Si Li","doi":"10.4310/atmp.2020.v24.n7.a2","DOIUrl":"https://doi.org/10.4310/atmp.2020.v24.n7.a2","url":null,"abstract":"We describe the coupling of holomorphic Chern-Simons theory at large N with Kodaira-Spencer gravity. We explain a new anomaly cancellation mechanism at all loops in perturbation theory for open-closed topological B-model. At one loop this anomaly cancellation is analogous to the Green-Schwarz mechanism. \u0000As an application, we introduce a type I version of Kodaira-Spencer theory in complex dimensions 3 and 5. In complex dimension 5, we show that it can only be coupled consistently at the quantum level to holomorphic Chern-Simons theory with gauge group SO(32). This is analogous to the Green-Schwarz mechanism for the physical type I string. This coupled system is conjectured to be a supersymmetric localization of type I string theory. In complex dimension 3, the required gauge group is SO(8).","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86044501","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}
引用次数: 24
Fully extended BV-BFV description of General Relativity in three dimensions 广义相对论在三维空间中完全扩展的BV-BFV描述
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-05-22 DOI: 10.4310/ATMP.2022.v26.n3.a2
G. Canepa, M. Schiavina
{"title":"Fully extended BV-BFV description of General Relativity in three dimensions","authors":"G. Canepa, M. Schiavina","doi":"10.4310/ATMP.2022.v26.n3.a2","DOIUrl":"https://doi.org/10.4310/ATMP.2022.v26.n3.a2","url":null,"abstract":"We compute the extension of the BV theory for three-dimensional General Relativity to all higher-codimension strata - boundaries, corners and vertices - in the BV-BFV framework. Moreover, we show that such extension is strongly equivalent to (nondegenerate) BF theory at all codimensions.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89792957","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}
引用次数: 11
Remarks on intersection numbers and integrable hierarchies, I: Quasi-triviality 交点数与可积层次的注释，I:拟平凡性
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-05-20 DOI: 10.4310/atmp.2020.v24.n5.a1
B. Dubrovin, Di Yang
{"title":"Remarks on intersection numbers and integrable hierarchies, I: Quasi-triviality","authors":"B. Dubrovin, Di Yang","doi":"10.4310/atmp.2020.v24.n5.a1","DOIUrl":"https://doi.org/10.4310/atmp.2020.v24.n5.a1","url":null,"abstract":"Explicit expression for quasi-triviality of scalar non-linear PDE is under consideration.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90754995","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}
引用次数: 9
Extremal isosystolic metrics with multiple bands of crossing geodesics 具有多个交叉测地线带的极端等收缩度量
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-03-28 DOI: 10.4310/atmp.2022.v26.n5.a7
Usman Naseer, B. Zwiebach
{"title":"Extremal isosystolic metrics with multiple bands of crossing geodesics","authors":"Usman Naseer, B. Zwiebach","doi":"10.4310/atmp.2022.v26.n5.a7","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n5.a7","url":null,"abstract":"We apply recently developed convex programs to find the minimal-area Riemannian metric on $2n$-sided polygons ($ngeq 3$) with length conditions on curves joining opposite sides. We argue that the Riemannian extremal metric coincides with the conformal extremal metric on the regular $2n$-gon. The hexagon was considered by Calabi. The region covered by the maximal number $n$ of geodesics bands extends over most of the surface and exhibits positive curvature. As $nto infty$ the metric, away from the boundary, approaches the well-known round extremal metric on $mathbb{RP}_2$. We extend Calabi's isosystolic variational principle to the case of regions with more than three bands of systolic geodesics. The extremal metric on $mathbb{RP}_2$ is a stationary point of this functional applied to a surface with infinite number of systolic bands.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90541911","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}
引用次数: 9
Ramond–Ramond fields and twisted differential K-theory Ramond-Ramond场和扭曲微分k理论
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-03-21 DOI: 10.4310/atmp.2022.v26.n5.a2
Daniel Grady, H. Sati
{"title":"Ramond–Ramond fields and twisted differential K-theory","authors":"Daniel Grady, H. Sati","doi":"10.4310/atmp.2022.v26.n5.a2","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n5.a2","url":null,"abstract":"We provide a systematic approach to describing the Ramond-Ramond (RR) fields as elements in twisted differential K-theory. This builds on a series of constructions by the authors on geometric and computational aspects of twisted differential K-theory, which to a large extent were originally motivated by this problem. In addition to providing a new conceptual framework and a mathematically solid setting, this allows us to uncover interesting and novel effects. Explicitly, we use our recently constructed Atiyah-Hirzebruch spectral sequence (AHSS) for twisted differential K-theory to characterize the RR fields and their quantization, which involves interesting interplay between geometric and topological data. We illustrate this with the examples of spheres, tori, and Calabi-Yau threefolds.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82647947","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}
引用次数: 16
Asymptotically flat extensions with charge 带电荷的渐近平面扩展
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-03-21 DOI: 10.4310/atmp.2019.v23.n8.a1
Aghil Alaee, Armando J. Cabrera Pacheco, Carla Cederbaum
{"title":"Asymptotically flat extensions with charge","authors":"Aghil Alaee, Armando J. Cabrera Pacheco, Carla Cederbaum","doi":"10.4310/atmp.2019.v23.n8.a1","DOIUrl":"https://doi.org/10.4310/atmp.2019.v23.n8.a1","url":null,"abstract":"The Bartnik mass is a notion of quasi-local mass which is remarkably difficult to compute. Mantoulidis and Schoen [2016] developed a novel technique to construct asymptotically flat extensions of minimal Bartnik data in such a way that the ADM mass of these extensions is well-controlled, and thus, they were able to compute the Bartnik mass for minimal spheres satisfying a stability condition. In this work, we develop extensions and gluing tools, a la Mantoulidis and Schoen, for time-symmetric initial data sets for the Einstein-Maxwell equations that allow us to compute the value of an ad-hoc notion of charged Barnik mass for suitable charged minimal Bartnik data.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75832121","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}
引用次数: 3
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