Instantons, Fermions and Chern-Simons Terms

TL;DR

This paper explores the effects of Chern-Simons interactions on instantons in five dimensions, revealing how they induce modifications in the quantum mechanics and moduli space dynamics of these solitonic particles.

Contribution

It demonstrates the induction of Chern-Simons terms in the ADHM quantum mechanics and describes instanton dynamics via geodesic motion influenced by a magnetic field.

Findings

Chern-Simons term induces a corresponding term in ADHM quantum mechanics.

Instanton dynamics are described by geodesic motion on moduli space with a magnetic field.

Magnetic field equals the first Chern character of an index bundle.

Abstract

In five spacetime dimensions, instantons are finite energy, solitonic particles. We describe the dynamics of these objects in the presence of a Chern-Simons interaction. For U(N) instantons, we show that the 5d Chern-Simons term induces a corresponding Chern-Simons term in the ADHM quantum mechanics. For SU(N) instantons, we provide a description in terms of geodesic motion on the instanton moduli space, modified by the presence of a magnetic field. We show that this magnetic field is equal to the first Chern character of an index bundle. All of these results are derived by a simple method which follows the fate of zero modes as fermions are introduced, made heavy, and subsequently integrated out.