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

A bstract We study the supersymmetric partition function on S 1 × 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.