弦理论中通过膜统一晶格模型、链接和量子几何朗兰

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Advances in Theoretical and Mathematical Physics Pub Date : 2019-10-02 DOI:10.4310/ATMP.2020.v24.n7.a1

M. Ashwinkumar, M. Tan

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引用次数: 6

摘要

我们解释了如何从IIA型弦理论中以ns5膜为尾的d4膜的一堆开始，通过t对偶性和相关世界体积理论的拓扑全纯性，联系(i) Costello的4d chen - simons理论实现的晶格模型，(ii)三维解析连续chen - simons理论中的链接，(iii) Kapustin-Witten利用4d N = 4规范理论及其量子群修正实现的量子几何朗兰兹对应。(iv)量子群/仿射Kac-Moody代数与Whittaker d -模/ w -代数之间的Gaitsgory-Lurie猜想。这在纯物理上通过弦理论中的膜，在可积系统的数学、几何拓扑、几何表示理论和量子代数之间架起了一座新的桥梁。

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Unifying lattice models, links and quantum geometric Langlands via branes in string theory

We explain how, starting with a stack of D4-branes ending on an NS5-brane in type IIA string theory, one can, via T-duality and the topological-holomorphic nature of the relevant worldvolume theories, relate (i) the lattice models realized by Costello's 4d Chern-Simons theory, (ii) links in 3d analytically-continued Chern-Simons theory, (iii) the quantum geometric Langlands correspondence realized by Kapustin-Witten using 4d N = 4 gauge theory and its quantum group modification, and (iv) the Gaitsgory-Lurie conjecture relating quantum groups/affine Kac-Moody algebras to Whittaker D-modules/W-algebras. This furnishes, purely physically via branes in string theory, a novel bridge between the mathematics of integrable systems, geometric topology, geometric representation theory, and quantum algebras.

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来源期刊

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

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.