Aspects of class-S theories




Yan, Fei, (Ph. D. in physics)

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This dissertation discusses certain aspects of class-S theories [1,2]. First we give an overview of class-S theories. Then we report on the study of product SCFTs in class-S theories. We first describe an algorithm to determine whether an isolated 4d N = 2 SCFT is a product of two (or more) theories and apply this algorithm to a large subset of class-S theories that have been catalogued. This part is based on joint work with Jacques Distler and Behzat Ergun [3]. Afterwards we report on some preliminary studies of the supersymmetric vacuum moduli space of product SCFTs. Finally we turn our attention to supersymmetric (half) line defects in 4d N = 2 theories. In particular we describe a close relation between the Schur index in the presence of a supersymmetric (half) line defect and the vacuum expectation value of such line defect in U(1) [subscript r]-invariant vacua of the theory compactified on a circle. We explicitly check such relation in some special class-S theories: the ArgyresDouglas theories of type (A₁, A₂), (A₁, A₄), (A₁, A₆), (A₁, D₃) and (A₁, D₅). This part is based on joint work with Andrew Neitzke [4].



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