Four-dimensional lens space index from two-dimensional chiral algebra

Abstract

We study the supersymmetric partition function on S-1 x L(r, 1), or the lens space index of four-dimensional N = 2 superconformal field theories and their connection to two-dimensional chiral algebras. We primarily focus on free theories as well as ArgyresDouglas theories of type (A(1), A(k)) and (A(1), D-k). We observe that in specific limits, the lens space index is reproduced in terms of the (refined) character of an appropriately twisted module of the associated two-dimensional chiral algebra or a generalized vertex operator algebra. The particular twisted module is determined by the choice of discrete holonomies for the flavor symmetry in four-dimensions.