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2017

Four-dimensional Lens Space Index from Two-dimensional Chiral Algebra

Fluder, Martin, Song, Jaewon

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We study the supersymmetric partition function on $S^1 \times L(r, 1)$, or the lens space index of four-dimensional $\mathcal{N}=2$ superconformal field theories and their connection to two-dimensional chiral algebras.

We primarily focus on free theories as well as Argyres-Douglas 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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