Tricritical behavior in the Chern-Simons-Ginzburg-Landau theory of self-dual Josephson junction arrays

Abstract

We examine the phase structure of a U(1)×U(1)-symmetric model in three dimensional space-time with a potential of sixth order in the scalar fields coupled to dynamic gauge fields with a mixed Chern-Simons term. Using a large N technique, we compute the quantum effective potential and the renormalization group functions of the various couplings to the next-to-leading order of the 1/N expansion in terms of the mixed Chern-Simons coefficient. The model has a phase which exhibits spontaneous breaking of scale symmetry accompanied by a massless dilaton which is a Goldstone mode. We explicitly show that the various sextic couplings beta functions vanish to leading order in the 1/N expansion; however, at the next order in the 1/N expansion, they exhibit nontrivial running that we analyze explicitly in terms of the mixed Chern–Simons coefficient. We demonstrate that the gauge fluctuations split the zeros of the beta functions and generate a variety of nontrivial fixed points. The stability of these fixed points and the requirement of the positivity of the renormalization group improved effective potential are also examined. Our study identifies a window in the parameter space of the mixed Chern-Simons coefficient where the renormalization group flow has a stable infrared fixed point where scale invariance is recovered.

Similar papers