2005/03/31 by Wolfgang Behr, Frank Meyer, Harold Steinacker · 1 citation
Physics and Astronomy · #BRST quantization #Black Holes and Theoretical Physics #Dirac fermion #Dirac operator #Gauge theory #Neutrino Physics Research #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Path integral formulation #Quantization (signal processing) #Regularization (linguistics) #Supersymmetric gauge theory #hep-th
paper · pdf · doi:10.1088/1126-6708/2005/07/040
published as JHEP 0507 (2005) 040 · 39 pages. V2-4: References added, typos fixed
arxiv created 2005/05/24 · openalex publication_date 2005/07/18 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We define U(n) gauge theory on fuzzy S2N x S2N as a multi-matrix model, which reduces to ordinary Yang-Mills theory on S2 x S2 in the commutative limit N -> infinity. The model can be used as a regularization of gauge theory on noncommutative R4θin a particular scaling limit, which is studied in detail. We also find topologically non-trivial U(1) solutions, which reduce to the known "fluxon" solutions in the limit of R4θ, reproducing their full moduli space. Other solutions which can be interpreted as 2-dimensional branes are also found. The quantization of the model is defined non-perturbatively in terms of a path integral which is finite. A gauge-fixed BRST-invariant action is given as well. Fermions in the fundamental representation of the gauge group are included using a formulation based on SO(6), by defining a fuzzy Dirac operator which reduces to the standard Dirac operator on S2 x S2 in the commutative limit. The chirality operator and Weyl spinors are also introduced.