Super Liouville conformal blocks from N=2 SU(2) quiver gauge theories

TL;DR

This paper extends the AGT correspondence to N=1 supersymmetric conformal blocks, deriving explicit superconformal blocks using modified instanton moduli spaces and Young diagrams with two cell types.

Contribution

It introduces a modification of the instanton moduli space to account for N=1 supersymmetry, providing explicit formulas for superconformal blocks.

Findings

Derived explicit N=1 superconformal blocks.

Identified the need for Z(2)-symmetry restriction.

Connected instanton partition functions to N=1 superconformal field theory.

Abstract

The conjecture about the correspondence between instanton partition functions in the N=2 SUSY Yang-Mills theory and conformal blocks of two-dimensional conformal field theories is extended to the case of the N=1 supersymmetric conformal blocks. We find that the necessary modification of the moduli space of instantons requires additional restriction of Z(2)-symmetry. This leads to an explicit form of the N=1 superconformal blocks in terms of Young diagrams with two sorts of cells.