Sigma-model limit of Yang-Mills instantons in higher dimensions

authored by

Andreas Deser, Olaf Lechtenfeld, Alexander D. Popov

Abstract

We consider the Hermitian Yang-Mills (instanton) equations for connections on vector bundles over a 2n-dimensional Kähler manifold X which is a product Y×. Z of p- and q-dimensional Riemannian manifold Y and Z with p+. q=2. n. We show that in the adiabatic limit, when the metric in the Z direction is scaled down, the gauge instanton equations on Y×. Z become sigma-model instanton equations for maps from Y to the moduli space M (target space) of gauge instantons on Z if q≥. 4. For q<. 4 we get maps from Y to the moduli space M of flat connections on Z. Thus, the Yang-Mills instantons on Y×. Z converge to sigma-model instantons on Y while Z shrinks to a point. Put differently, for small volume of Z, sigma-model instantons on Y with target space M approximate Yang-Mills instantons on Y×. Z.

Organisation(s)

Institut für Theoretische Physik
Riemann Center for Geometry and Physics

Type

Artikel

Journal

Nuclear Physics B

Volume

894

Pages

361-373

No. of pages

13

ISSN

0550-3213

Publication date

2015

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Kern- und Hochenergiephysik

Electronic version(s)

https://doi.org/10.1016/j.nuclphysb.2015.03.009 (Access: Offen)