A 5d/2d/4d correspondence

TL;DR

This paper proposes a novel correspondence linking 2D (0,4) sigma models, 4D N=4 U(r) Yang-Mills theory, and insights from 5D supersymmetric gauge theories, with proofs for the r=1 case.

Contribution

It introduces a new 5d/2d/4d correspondence connecting different gauge theories and geometric structures, supported by rigorous tests and proofs for specific cases.

Findings

Partition functions for r=1 are proven equal.

The correspondence is supported by multiple tests.

Insights from M-theory underpin the proposal.

Abstract

We propose a correspondence between two-dimensional (0,4) sigma models with target space the moduli spaces of r monopoles, and four-dimensional N=4, U(r) Yang-Mills theory on del Pezzo surfaces. In particular, the two- and four-dimensional BPS partition functions are argued to be equal. The correspondence relies on insights from five-dimensional supersymmetric gauge theory and its geometric engineering in M-theory, hence the name "5d/2d/4d correspondence". We provide various tests of our proposal. The most stringent ones are for r=1, for which we prove the equality of partition functions.