Generalized Gross-Neveu Universality Class with Non-Abelian Symmetry

TL;DR

This paper extends the analysis of the Gross-Neveu universality class by incorporating non-Abelian symmetries, providing a comprehensive framework for calculating critical exponents across various Lie groups and fermion representations.

Contribution

It introduces a generalized approach to compute critical exponents in the Gross-Neveu universality class with non-Abelian symmetry groups using large N techniques.

Findings

Derived critical exponents for various Lie groups.

Unified expressions applicable to different fermion representations.

Recovers known results in the abelian limit.

Abstract

We use the large $N$ critical point formalism to compute $d$-dimensional critical exponents at several orders in $1/N$ in an Ising Gross-Neveu universality class where the core interaction includes a Lie group generator. Specifying a particular symmetry group or taking the abelian limit of the final exponents recovers known results but also provides expressions for any Lie group or fermion representation.