N=2 superconformal blocks and instanton partition functions

TL;DR

This paper develops a method to compute N=2 superconformal blocks in 2d conformal field theories by linking representation theory and instanton partition functions, providing explicit combinatorial formulas in a specific limit.

Contribution

It introduces a novel approach connecting N=2 superconformal blocks with affine sl(2) algebra and instanton partition functions, leading to explicit combinatorial expressions.

Findings

Derived combinatorial formulas for N=2 superconformal blocks in the Gaiotto limit.

Established a relation between N=2 superconformal algebra and affine sl(2) algebra.

Linked conformal blocks to instanton partition functions in 4d N=2 gauge theories.

Abstract

We consider the problem of computing (irregular) conformal blocks in 2d CFTs whose chiral symmetry algebra is the N=2 superconformal algebra. Our construction uses two ingredients: (i) the relation between the representation theories of the N=2 superconformal algebra and the affine sl(2) algebra, extended to the level of the conformal blocks, and (ii) the relation between affine sl(2) conformal blocks and instanton partition functions in the 4d N=2 SU(2) gauge theory with a surface defect. By combining these two facts we derive combinatorial expressions for the N=2 superconformal blocks in the Gaiotto limit.