Large-c superconformal torus blocks

TL;DR

This paper analyzes large central charge limits of superconformal blocks on a torus in N=1 SCFT2, deriving explicit forms of various superblocks and connecting them to known differential equations like the Heun equation.

Contribution

It explicitly calculates three types of superblocks in the large-c limit and relates them through differential equations, extending understanding of superconformal symmetry structures.

Findings

Derived explicit forms of osp(1|2) global, light, and heavy-light superblocks.

Connected superblocks to Heun differential equations.

Showed osp(1|2) superblocks approximate non-supersymmetric sl(2) blocks at large conformal dimensions.

Abstract

We study large-c SCFT2 on a torus specializing to one-point superblocks in the N=1 Neveu-Schwarz sector. Considering different contractions of the Neveu-Schwarz superalgebra related to the large central charge limit we explicitly calculate three superblocks, osp(1|2) global, light, and heavy-light superblocks, and show that they are related to each other. We formulate the osp(1|2) superCasimir eigenvalue equations and identify their particular solutions as the global superblocks. It is shown that the resulting differential equations are the Heun equations. We study exponentiated global superblocks arising at large conformal dimensions and demonstrate that in the leading approximation the osp(1|2) superblocks are equal to the non-supersymmetric sl(2) block.