Large-N analysis of the critical behavior of the topological Ginzburg-Landau theory of self-dual Josephson junction arrays

Abstract

Using large-N technique at fixed dimension (d=3), I examine the multicritical behavior of a U(N/2)×U(N/2) Ginzburg-Landau theory of two multicomponent complex fields interacting through gauge fields described by Maxwell terms and a mixed Chern-Simons term. This model is relevant to the dynamics of Cooper pairs and vortices in a self-dual Josephson junction array system near its superconductor-insulator quantum transition. I present calculations of the various critical exponents including 1/N corrections to the N=∞ saddle point. I investigate in the scaling region the behavior of the renormalized zero-momentum four-point quartic couplings u and w in the action, and I calculate the 1/N correction to the β-functions and their fixed-point values. It is shown that the decoupled fixed point is destabilized in the presence of the mixed Chern-Simons term at the next-to-leading order. Finally, I examine the universal character of the conductivity at the critical point up to the next-to-leading order in 1/N expansion.

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