Non-Abelian sigma models from Yang–Mills theory compactified on a circle

authored by

Tatiana A. Ivanova, Olaf Lechtenfeld, Alexander D. Popov

Abstract

We consider SU(N) Yang–Mills theory on R^2,1×S¹, where S¹ is a spatial circle. In the infrared limit of a small-circle radius the Yang–Mills action reduces to the action of a sigma model on R^2,1 whose target space is a 2(N−1)-dimensional torus modulo the Weyl-group action. We argue that there is freedom in the choice of the framing of the gauge bundles, which leads to more general options. In particular, we show that this low-energy limit can give rise to a target space SU(N)×SU(N)/Z_N. The latter is the direct product of SU(N) and its Langlands dual SU(N)/Z_N, and it contains the above-mentioned torus as its maximal Abelian subgroup. An analogous result is obtained for any non-Abelian gauge group.

Organisation(s)

Institut für Theoretische Physik
Riemann Center for Geometry and Physics

External Organisation(s)

Joint Institute for Nuclear Research (JINR)

Type

Artikel

Journal

Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

Volume

781

Pages

322-326

No. of pages

5

ISSN

0370-2693

Publication date

10.06.2018

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Kern- und Hochenergiephysik

Electronic version(s)

https://doi.org/10.48550/arXiv.1803.07322 (Access: Offen)
https://doi.org/10.1016/j.physletb.2018.04.013 (Access: Offen)
https://doi.org/10.15488/3368 (Access: Offen)