Strong-weak coupling duality in non-abelian gauge theories

TL;DR

This paper reviews electric-magnetic duality in non-abelian gauge theories, focusing on N=2 supersymmetric theories, and presents new exact calculations of eta invariants using supersymmetry properties.

Contribution

It introduces new methods for computing eta invariants in monopole backgrounds via supersymmetric one-loop calculations, simplifying previous approaches.

Findings

Exact eta invariant computations using N=2 supersymmetry

Simplification of monopole-related calculations

Applications to charge confinement and chiral symmetry breaking

Abstract

This is a general introduction to electric-magnetic duality in non-abelian gauge theories. In chapter I, I review the general ideas which led in the late 70s to the idea of electric/magnetic duality in quantum field theory. In chapters II and III, I focus mainly on N=2 supersymmetric theories. I present the lagrangians and explain in more or less detail the non-renormalization theorems, rigid special geometry, supersymmetric instanton calculus, charge fractionization, the semiclassical theory of monopoles, duality in Maxwell theory and the famous Seiberg-Witten solution. I discuss various physical applications, as electric charge confinement, chiral symmetry breaking or non-trivial superconformal theories in four dimensions. In Section II.3 new material is presented, related to the computation of the eta invariant of certain Dirac operators coupled minimally to non-trivial monopole field configurations. I explain how these invariants can be obtained exactly by a one-loop calculation in a suitable N=2 supersymmetric gauge theory. This is an unexpected application of the holomorphy properties of N=2 supersymmetry, and constitutes a tremendous simplification of the usual computation. An expanded version of these new results will be published soon.