| Summary: | Abstract We study the supersymmetric partition function on S 1 × L(r, 1), or the lens space index of four-dimensional N=2 $$ \mathcal{N}=2 $$ 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.
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