2006/06/30 by Badis Ydri · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2006.10.030
published as Nucl.Phys.B762:148-188,2007 · 46 pages,4 figures,typos corrected,references added
arxiv created 2006/09/25 · openalex publication_date 2006/11/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is found that noncommutative U(1) gauge field on the fuzzy sphere S2N is equivalent in the quantum theory to a commutative 2-dimensional U(N) gauge field on a lattice with two plaquettes in the axial gauge A1=0. This quantum equivalence holds in the fuzzy sphere-weak coupling phase in the limit of infinite mass of the scalar normal component of the gauge field. The doubling of plaquettes is a natural consequence of the model and it is reminiscent of the usual doubling of points in Connes standard model. In the continuum large N limit the plaquette variable W approaches the identity 12N and as a consequence the model reduces to a simple matrix model which can be easily solved. We compute the one-plaquette critical point and show that it agrees with the observed value α_*=3.35. We compute the quantum effective potential and the specific heat for U(1) gauge field on the fuzzy sphere S2N in the 1/N expansion using this one-plaquette model. In particular the specific heat per one degree of freedom was found to be equal to 1 in the fuzzy sphere-weak coupling phase of the gauge field which agrees with the observed value 1 seen in Monte Carlo simulation. This value of 1 comes precisely because we have 2 plaquettes approximating the NC U(1) gauge field on the fuzzy sphere.