Magnificent Four with Colors

TL;DR

This paper explores a supersymmetric gauge theory on Calabi-Yau fourfolds, proposing a conjectural formula for its partition function, which reveals new insights into higher rank Donaldson-Thomas theory and its parameter dependencies.

Contribution

It introduces an explicit conjectural formula for the partition function of a rank N supersymmetric theory with matter on Calabi-Yau fourfolds, linking it to higher rank Donaldson-Thomas theory.

Findings

Proposed an explicit formula for the partition function Z.

Found that Z has a free field representation.

Discovered simple dependence of Z on Coulomb and mass parameters.

Abstract

We study the rank N magnificent four theory, which is the supersymmetric localization of U(N) super-Yang-Mills theory with matter (a super-group U(N|N) gauge theory) on a Calabi-Yau fourfold. Our theory contains the higher rank Donaldson-Thomas theory of threefolds. We conjecture an explicit formula for the partition function Z, and report on the performed checks. The partition function Z has a free field representation. Surprisingly, it depends on the Coulomb and mass parameters in a simple way. We also clarify the definition of the instanton measure.