Instantons and 2d Superconformal field theory

TL;DR

This paper explores a novel correspondence linking 4D supersymmetric gauge theories with 2D superconformal field theories, specifically constructing a super Liouville conformal block through instanton moduli space analysis.

Contribution

It introduces a new construction of super Liouville conformal blocks using a conjectural relation between instanton moduli spaces and algebraic structures, confirming the conjecture through fixed point counting.

Findings

Confirmed the conjectural relation between instanton moduli spaces and algebraic representations.

Constructed four-point N=1 super Liouville conformal block for specific parameters.

Validated the correspondence by matching fixed point counts with algebraic dimensions.

Abstract

A recently proposed correspondence between 4-dimensional N=2 SUSY SU(k) gauge theories on R^4/Z_m and SU(k) Toda-like theories with Z_m parafermionic symmetry is used to construct four-point N=1 super Liouville conformal block, which corresponds to the particular case k=m=2. The construction is based on the conjectural relation between moduli spaces of SU(2) instantons on R^4/Z_2 and algebras like \hat{gl}(2)_2\times NSR. This conjecture is confirmed by checking the coincidence of number of fixed points on such instanton moduli space with given instanton number N and dimension of subspace degree N in the representation of such algebra.