Liouville Correlation Functions from Four-dimensional Gauge Theories

TL;DR

This paper proposes a new conjecture linking Liouville theory correlation functions to Nekrasov partition functions of specific N=2 SCFTs, with extensive tests at genus 0 and 1.

Contribution

It introduces a novel conjecture connecting Liouville conformal blocks with Nekrasov partition functions for certain 4D gauge theories.

Findings

The conjecture is supported by extensive tests at genus 0 and 1.

The proposed expression matches known results in specific cases.

Provides a new bridge between 2D CFT and 4D gauge theories.

Abstract

We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of N=2 SCFTs recently defined by one of the authors. We conduct extensive tests of the conjecture at genus 0,1.