Quantum effective potential for U(1) fields on S^2_L X S^2_L

TL;DR

This paper calculates the one-loop effective potential for noncommutative U(1) gauge fields on a product of two spheres, revealing a phase transition from a four-dimensional space to a matrix phase driven by quantum fluctuations.

Contribution

It introduces a novel phase transition in noncommutative gauge theory on S^2_L x S^2_L, showing the collapse of spheres into a matrix phase under quantum effects.

Findings

Existence of a phase transition from space to matrix phase.

Transition occurs at infinite gauge coupling when normal component mass goes to infinity.

Quantum fluctuations induce the collapse of the spherical geometry.

Abstract

We compute the one-loop effective potential for noncommutative U(1) gauge fields on S^2_L X S^2_L. We show the existence of a novel phase transition in the model from the 4-dimensional space S^2_L X 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 X S^2_L is sent to infinity.