论文标题
4d Chern-Simons理论是3D TODA理论，以及3D-2D对应关系
4d Chern-Simons Theory as a 3d Toda Theory, and a 3d-2d Correspondence
论文作者
论文摘要
我们表明，由Costello，Witten和Yamazaki研究的四维Chern-Simons理论是，具有NAHM Polet型边界条件，这是边界理论的双重偶，这是TODA理论的三维类似物，具有新颖的3D W-Algebra对称性。 By embedding four-dimensional Chern-Simons theory in a partial twist of the five-dimensional maximally supersymmetric Yang-Mills theory on a manifold with corners, we argue that this three-dimensional Toda theory is dual to a two-dimensional topological sigma model with A-branes on the moduli space of solutions to the Bogomolny equations.这提供了一种新型的3D-2D对应关系，除其他数学意义外，还揭示了3D W-Algebra的模块是Bogomolny Moduli空间上某些全态函数的量化代数的模块。
We show that the four-dimensional Chern-Simons theory studied by Costello, Witten and Yamazaki, is, with Nahm pole-type boundary conditions, dual to a boundary theory that is a three-dimensional analogue of Toda theory with a novel 3d W-algebra symmetry. By embedding four-dimensional Chern-Simons theory in a partial twist of the five-dimensional maximally supersymmetric Yang-Mills theory on a manifold with corners, we argue that this three-dimensional Toda theory is dual to a two-dimensional topological sigma model with A-branes on the moduli space of solutions to the Bogomolny equations. This furnishes a novel 3d-2d correspondence, which, among other mathematical implications, also reveals that modules of the 3d W-algebra are modules for the quantized algebra of certain holomorphic functions on the Bogomolny moduli space.
