2007/01/31 by Harold Steinacker, Richard J. Szabo · 16 citations
Mathematics · Physics and Astronomy · #Abelian group #Black Holes and Theoretical Physics #Fuzzy logic #Fuzzy sphere #Gauge theory #Homotopy and Cohomology in Algebraic Topology #Limit (mathematics) #Noncommutative and Quantum Gravity Theories #Partition (number theory) #Partition function (quantum field theory) #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/s00220-007-0386-0
published in Communications in Mathematical Physics 278(1), 193-252 (Springer Science+Business Media) · 55 pages. V2: references added; V3: minor corrections, reference added; Final version to be published in Communications in Mathematical Physics
arxiv created 2007/05/08 · openalex publication_date 2007/11/19 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.