JT重力与随机矩阵理论的系综

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
D. Stanford, E. Witten
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引用次数: 222

摘要

我们将最近发现的JT引力与双尺度随机矩阵理论之间的关系推广到边界理论可能具有时间反转对称性和可能具有或不具有超对称性的费米子的情况。JT重力与矩阵系综之间的匹配取决于假设的对称性。边界理论中的时间反转对称性意味着在体中必须考虑不可定向的时空。在这种情况下,JT引力的配分函数仍然与共形结构模空间的体积有关,但这个体积有量子校正,必须使用Reidemeister-Ray-Singer“扭转”来计算。边界理论中费米子的存在(因此具有对称性$(-1)^F$)意味着体具有自旋或销子结构。边界的超对称性意味着体理论与JT超引力有关,并且与超黎曼曲面而非普通黎曼曲面的模空间体积有关。在所有情况下,我们将JT重力或超重力与适当的随机矩阵系综相匹配。所有十个标准随机矩阵合奏都出现了——三个戴森合奏和七个Altland-Zirnbauer合奏。为了便于分析,我们扩展到在厄米矩阵的原始Wigner-Dyson系综中最熟悉的其他系综技术。我们还将Mirzakhani关于普通模空间体积的递推推广到超黎曼曲面的情况。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
JT gravity and the ensembles of random matrix theory
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.
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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
期刊介绍: Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.
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