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arXiv · 1811.11772

On the Correspondence between Surface Operators in Argyres-Douglas Theories and Modules of Chiral Algebra

Takahiro Nishinaka·Shinya Sasa·Rui-Dong Zhu
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Abstract

We compute the Schur index of Argyres-Douglas theories of type $(A_{N-1},A_{M-1})$ with surface operators inserted, via the Higgsing prescription proposed by D. Gaiotto, L. Rastelli and S. S. Razamat. These surface operators are obtained by turning on position-dependent vacuum expectation values of operators in a UV theory which can flow to the Argyres-Douglas theories. We focus on two series of $(A_{N-1},A_{M-1})$ theories; one with ${\rm gcd}(N,M)=1$ and the other with $M=N(k-1)$ for an integer $k\geq 2$. For these two series of Argyres-Douglas theories, our results are identical to the characters of non-vacuum modules of the associated 2d chiral algebras, which explicitly confirms a remarkable correspondence recently discovered by C. Cordova, D. Gaiotto and S.-H. Shao.

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Takahiro Nishinaka, Shinya Sasa, Rui-Dong Zhu. 2018-11-28. On the Correspondence between Surface Operators in Argyres-Douglas Theories and Modules of Chiral Algebra. https://doi.org/10.1007/jhep03(2019)091

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