Abstract :
It is found that noncommutative image gauge field on the fuzzy sphere image is equivalent in the quantum theory to a commutative 2-dimensional image gauge field on a lattice with two plaquettes in the axial gauge image. 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 image 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 image. We compute the quantum effective potential and the specific heat for image gauge field on the fuzzy sphere image in the image 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 image gauge field on the fuzzy sphere.
