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2019

Chiral Algebra, Localization, Modularity, Surface defects, And All That

Dedushenko, Mykola, Fluder, Martin

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We study the 2D vertex operator algebra (VOA) construction in 4D $\mathcal{N}=2$ superconformal field theories (SCFT) on $S^3 \times S^1$, focusing both on old puzzles as well as new observations.

The VOA lives on a two-torus $\mathbb{T}^2\subset S^3\times S^1$, it is $\frac12\mathbb{Z}$-graded, and this torus is equipped with the natural choice of spin structure (1,0) for the $\mathbb{Z} +\frac12$-graded operators, corresponding to the NS sector vacuum character.
By analyzing the possible refinements of the Schur index that preserve the VOA, we find that it admits discrete deformations, which allow access to the remaining spin structures (1,1), (0,1) and (0,0), of which the latter two involve the inclusion of a particular surface defect.
For Lagrangian theories, we perform the detailed analysis: we describe the natural supersymmetric background, perform localization, and derive the gauged symplectic boson action on a torus in any spin structure.

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