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

Abstract

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.

47 pages; v2: minor corrections, published version

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• Schur sector of Argyres-Douglas theory and $W$-algebra
• A 2d (0,2) appetizer
• Vanishing OPE Coefficients in 4d N=2 SCFTs
• Classification of large N superconformal gauge theories with a dense spectrum
• On dimensional reduction of 4d N=1 Lagrangians for Argyres-Douglas theories
• OPE Selection Rules for Schur Multiplets in 4D $\mathcal{N}=2$ Superconformal Field Theories
• Testing Macdonald Index as a Refined Character of Chiral Algebra
• Closed form fermionic expressions for the Macdonald index
• The Chiral Algebra of Genus Two Class $\mathcal{S}$ Theory
• Lens space index and global properties for 4d N = 2 models