Advances in Theoretical and Mathematical Physics最新文献_第9页

A nonabelian duality for (higher) gauge theories (高)规范理论的非abel对偶性

IF 1.5 4区物理与天体物理

Advances in Theoretical and Mathematical Physics Pub Date : 2019-09-13 DOI: 10.4310/ATMP.2021.v25.n1.a5

Ján Pulmann, Pavol vSevera, F. Valach

引用次数: 7

Boundary $mathcal{N} = 2$ theory, Floer homologies, affine algebras, and the Verlinde formula 边界$mathcal{N} = 2$理论，花同调，仿射代数，和Verlinde公式

IF 1.5 4区物理与天体物理

Advances in Theoretical and Mathematical Physics Pub Date : 2019-09-09 DOI: 10.4310/ATMP.2021.v25.n1.a1

M. Ashwinkumar, Kee-Seng Png, M. Tan

引用次数: 0

A proposal for nonabelian $(0,2)$ mirrors 非abel $(0,2)$镜像的一个建议

IF 1.5 4区物理与天体物理

Advances in Theoretical and Mathematical Physics Pub Date : 2019-08-16 DOI: 10.4310/ATMP.2021.v25.n6.a4

W. Gu, J. Guo, E. Sharpe

引用次数: 10

Invertible field transformations with derivatives: necessary and sufficient conditions 带导数的可逆场变换:充要条件

IF 1.5 4区物理与天体物理

Advances in Theoretical and Mathematical Physics Pub Date : 2019-07-29 DOI: 10.4310/atmp.2021.v25.n2.a2

E. Babichev, K. Izumi, Norihiro Tanahashi, Masahide Yamaguchi

引用次数: 11

Twisted gauge fields 扭曲规范场

IF 1.5 4区物理与天体物理

Advances in Theoretical and Mathematical Physics Pub Date : 2019-07-19 DOI: 10.4310/ATMP.2021.v25.n6.a2

J. Franccois

引用次数: 2

On the counting of $O(N)$ tensor invariants 关于O(N)张量不变量的计数

IF 1.5 4区物理与天体物理

Advances in Theoretical and Mathematical Physics Pub Date : 2019-07-10 DOI: 10.4310/ATMP.2020.v24.n4.a1

R. C. Avohou, J. B. Geloun, N. Dub

{"title":"On the counting of $O(N)$ tensor invariants","authors":"R. C. Avohou, J. B. Geloun, N. Dub","doi":"10.4310/ATMP.2020.v24.n4.a1","DOIUrl":"https://doi.org/10.4310/ATMP.2020.v24.n4.a1","url":null,"abstract":"$O(N)$ invariants are the observables of real tensor models. We use regular colored graphs to represent these invariants, the valence of the vertices of the graphs relates to the tensor rank. We enumerate $O(N)$ invariants as $d$-regular graphs, using permutation group techniques. We also list their generating functions and give (software) algorithms computing their number at an arbitrary rank and an arbitrary number of vertices. As an interesting property, we reveal that the algebraic structure which organizes these invariants differs from that of the unitary invariants. The underlying topological field theory formulation of the rank $d$ counting shows that it corresponds to counting of coverings of the $d-1$ cylinders sharing the same boundary circle and with $d$ defects. At fixed rank and fixed number of vertices, an associative semi-simple algebra with dimension the number of invariants naturally emerges from the formulation. Using the representation theory of the symmetric group, we enlighten a few crucial facts: the enumeration of $O(N)$ invariants gives a sum of constrained Kronecker coefficients; there is a representation theoretic orthogonal base of the algebra that reflects its dimension; normal ordered 2-pt correlators of the Gaussian models evaluate using permutation group language, and further, via representation theory, these functions provide other representation theoretic orthogonal bases of the algebra.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"26 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80277111","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

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":"81 1","pages":""},"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":"28 1","pages":""},"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

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

引用次数: 6