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arXiv · 1801.08316

Argyres-Douglas Theories, Modularity of Minimal Models and Refined Chern-Simons

Can Kozçaz·Shamil Shakirov·Wenbin Yan
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Abstract

The Coulomb branch indices of Argyres-Douglas theories on $L(k,1)\times S^{1}$ are recently identified with matrix elements of modular transforms of certain $2d$ vertex operator algebras in a particular limit. A one parameter generalization of the modular transformation matrices of $(2N+3,2)$ minimal models are proposed to compute the full Coulomb branch index of $(A_{1},A_{2N})$ Argyres-Douglas theories on the same space. Morever, M-theory construction of these theories suggests direct connection to the refined Chern-Simons theory. The connection is made precise by showing how the modular transformation matrices of refined Chern-Simons theory are related to the proposed generalized ones for minimal models and the identification of Coulomb branch indices with the partition function of the refined Chern-Simons theory.

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Can Kozçaz, Shamil Shakirov, Wenbin Yan. 2018-01-25. Argyres-Douglas Theories, Modularity of Minimal Models and Refined Chern-Simons. https://arxiv.org/abs/1801.08316

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