Critical behavior of supersymmetric O(N) models in the large-N limit

TL;DR

This paper derives and solves an exact RG equation for supersymmetric O(N) models in three dimensions at large N, classifying fixed points and calculating critical exponents, with implications for related scalar theories.

Contribution

It provides the first exact solution of the RG flow for supersymmetric O(N) models in the large-N limit, including classification of fixed points and critical exponents.

Findings

Exact fixed-point solutions classified by an exactly marginal coupling

Identification of regimes with unique, multiple, or no fixed points

Determination of critical exponents for superpotential and scalar potential

Abstract

We derive a supersymmetric renormalization group (RG) equation for the scale-dependent superpotential of the supersymmetric O(N) model in three dimensions. For a supersymmetric optimized regulator function we solve the RG equation for the superpotential exactly in the large-N limit. The fixed-point solutions are classified by an exactly marginal coupling. In the weakly coupled regime there exists a unique fixed point solution, for intermediate couplings we find two separate fixed point solutions and in the strong coupling regime no globally defined fixed-point potentials exist. We determine the exact critical exponents both for the superpotential and the associated scalar potential. Finally we relate the high-temperature limit of the four-dimensional theory to the Wilson-Fisher fixed point of the purely scalar theory.