Four-dimensional QCD and fiberwise duality

TL;DR

This paper introduces a fiberwise duality transformation that maps the partition function of four-dimensional QCD on a product of tori into a sigma-model with a specific target space, revealing new geometric insights.

Contribution

It presents a novel fiberwise duality approach that reformulates 4D QCD partition functions as sigma-models with geometric target spaces.

Findings

Partition function of 4D QCD on tori transformed into a sigma-model.

Identification of the target space as the cotangent space of unitary connections.

Provides a new geometric perspective on QCD via duality.

Abstract

We transform, by means of a fiberwise duality, the partition function of QCD on a product of two two-tori, into a four-dimensional sigma-model, whose target space is the cotangent space of unitary connections on the fiber torus fiberwise.