Quantum effective potential for U ( 1 ) fields on S 2 L × S 2 L

We compute the one-loop effective potential for noncommutative U (1) gauge fields on S 2 L ×S 2 L. We show the existence of a novel phase transition in the model from the 4−dimensional space S 2 L ×S 2 L to a matrix phase where the spheres collapse under the effect of quantum fluctuations. It is also shown that the transition to the matrix phase occurs at infinite value of the gauge coupling constant when the mass of the two normal components of the gauge field on S 2 L ×S 2 L is sent to infinity.