Unstable Bundles in Quantum Field Theory

TL;DR

This paper explores the connection between unstable bundles and classical gauge configurations like monopoles and instantons, suggesting their significance in quantum vacuum states and quark confinement mechanisms in quantum field theory.

Contribution

It introduces a novel perspective linking unstable bundles to key classical solutions in quantum field theory across multiple dimensions.

Findings

Unstable bundles relate to monopoles, sphalerons, and instantons.

Classical configurations appear as nodes in quantum vacuum states.

Implications for quark confinement in QCD.

Abstract

The relation between connections on 2-dimensional manifolds and holomorphic bundles provides a new perspective on the role of classical gauge fields in quantum field theory in two, three and four dimensions. In particular we show that there is a close relation between unstable bundles and monopoles, sphalerons and instantons. Some of these classical configurations emerge as nodes of quantum vacuum states in non-confining phases of \qft which suggests a relevant role for those configurations in the mechanism of quark confinement in QCD.