Abstract
We study the supersymmetric partition function on S1 × 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 ArgyresDouglas theories of type (A1, Ak) and (A1, Dk). 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.
Highlights
Under this map, various observables of the four-dimensional theory, which are invariant under exactly marginal deformations, are mapped to quantities in the two-dimensional chiral algebra [2,3,4]
We study the supersymmetric partition function on S1 × 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 observe that in specific limits, the lens space index is reproduced in terms of the character of an appropriately twisted module of the associated two-dimensional chiral algebra or a generalized vertex operator algebra
Summary
The chiral algebra for the free N = 2 hypermultiplet is given by the system of symplectic bosons or equivalently a β − γ system with (hβ, hγ). Aspects of this theory are discussed in detail, for example in [41, 42]. Let us first write down some generalities about the chiral algebra corresponding to the free hypermultiplet:. The case with λ = 0 for the twisted module is special, and the character is given by (qa; q)−1(q/a; q)−1 This case is not connected to the lens index as we shall see later.
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