Localization for Yang-Mills theory on the fuzzy sphere

Autor(en)

Harold Steinacker, Richard Szabo

Abstrakt

We present a new model for Yang-Mills theory on the fuzzy sphere in which the configuration space of gauge fields is given by a coadjoint orbit. In the classical limit it reduces to ordinary Yang-Mills theory on the sphere. We find all classical solutions of the gauge theory and use nonabelian localization techniques to write the partition function entirely as a sum over local contributions from critical points of the action, which are evaluated explicitly. The partition function of ordinary Yang-Mills theory on the sphere is recovered in the classical limit as a sum over instantons. We also apply abelian localization techniques and the geometry of symmetric spaces to derive an explicit combinatorial expression for the partition function, and compare the two approaches. These extend the standard techniques for solving gauge theory on the sphere to the fuzzy case in a rigorous framework.

Organisation(en)

Teilchenphysik

Externe Organisation(en)

University of Edinburgh

Journal

Communications in Mathematical Physics

Band

278

Seiten

193-252

Anzahl der Seiten

60

ISSN

0010-3616

DOI

https://doi.org/10.1007/s00220-007-0386-0

Publikationsdatum

2008

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Link zum Portal

https://ucris.univie.ac.at/portal/de/publications/localization-for-yangmills-theory-on-the-fuzzy-sphere(32a0d438-8788-4440-a77c-6b8c2f6a3496).html