Geometric Langlands Twists of N = 4 Gauge Theory from Derived Algebraic Geometry

B-扭转 Langlands TQFT 的拟代数量子化

Quasi-algebraic quantization for the B-twist Langlands TQFT

该研究为 Langlands QFT 的 B-扭转构造超全纯边界条件，通过定义拟代数层范畴并构造 Moore--Tachikawa 范畴的表示，推进相对 Langlands 纲领。

来自 N = 4 超杨-米尔斯理论的量子几何朗兰兹范畴

Quantum Geometric Langlands Categories from N = 4 Super Yang-Mills Theory

本文利用导出代数几何和全纯陈-西蒙斯理论描述 N = 4 超杨-米尔斯理论的超对称扭转族，并通过范畴几何量子化给出量子几何朗兰兹对应中扭转 D-模范畴的量子场论综合。

量子朗兰兹对偶与共形域论

Quantum Langlands duality and conformal field theory

Drinfeld提出了几何Langlands对应及其量子形变的理论。我们改进了这些结构，并提出了它们与代数共形域论的关系。

Notes on the Twistor $\mathbf P^1$

Remarkably, the twistor $\mathbf P^1$ occurs as a fundamental object in both four-dimensional space-time geometry and in number theory. In Euclidean signature twistor theory it is how one describes space-time points. In recent work by Fargues and Scholze on the local Langlands conjecture using geometric Langlands on the Fargues-Fontaine curve, the twistor $\mathbf P^1$ appears as the analog of this curve at the infinite prime. These notes are purely expository, written with the goal of explaining, in a form accessible to both mathematicians and physicists, various different ways in which the t…

A Physical Origin for Singular Support Conditions in Geometric Langlands Theory

We explain how the nilpotent singular support condition introduced into the geometric Langlands conjecture by Arinkin and Gaitsgory arises naturally from the point of view of N = 4 supersymmetric gauge theory. We define what it means in topological quantum field theory to restrict a category of boundary conditions to the full subcategory of objects compatible with a fixed choice of vacuum, both in functorial field theory and in the language of factorization algebras. For B-twisted N = 4 gauge theory with gauge group G, the moduli space of vacua is equivalent to h*/W , and the nilpotent singula…

Twisted compactifications of 3d N = 4 theories and conformal blocks

Three-dimensional N = 4 supersymmetric quantum field theories admit two topological twists, the Rozansky-Witten twist and its mirror. Either twist can be used to define a supersymmetric compactification on a Riemann surface and a corre- sponding space of supersymmetric ground states. These spaces of ground states can play an interesting role in the Geometric Langlands program. We propose a description of these spaces as conformal blocks for certain non-unitary Vertex Operator Algebras and test our conjecture in some important examples. The two VOAs can be constructed respectively from a UV Lag…