Instantons, Fermions and Chern-Simons Terms
High Energy Physics - Theory
2009-12-04 v2
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.
Cite
@article{arxiv.0804.1772,
title = {Instantons, Fermions and Chern-Simons Terms},
author = {Benjamin Collie and David Tong},
journal= {arXiv preprint arXiv:0804.1772},
year = {2009}
}
Comments
12 pages. v2: factor of 2 corrected