On the correspondence between surface operators in Argyres-Douglas theories and modules of chiral algebra

• Published in: The journal of high energy physics Vol. 2019; no. 3; pp. 1 - 29
• Main Authors: Nishinaka, Takahiro, Sasa, Shinya, Zhu, Rui-Dong
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2019; Springer Nature B.V; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Conformal and W Symmetry; Conformal Field Theory; Duality in Gauge Field Theories; Elementary Particles; High energy physics; Modules; Operators (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Supersymmetric Gauge Theory; Conformal and W Symmetry; Duality in Gauge Field Theories; Conformal Field Theory; Supersymmetric Gauge Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP03(2019)091

A bstract 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 gcd( N, M ) = 1 and the other with M = N ( k − 1) for an integer k ≥ 2. Our results are identified with 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.