Exact renormalization group study of fermionic theories

TL;DR

This paper develops an exact renormalization group framework for fermionic theories, deriving a Grassmann-based ERG equation, and analyzes fixed points and critical exponents in the two-dimensional chiral Gross-Neveu model.

Contribution

It introduces a Grassmann version of the ERG equation for fermionic theories and provides analytical and numerical solutions for fixed points and critical exponents.

Findings

Analytical fixed point solutions in the large N limit.

Numerical fixed point solutions for finite N.

Identification of a known and potentially new fixed point solution.

Abstract

The exact renormalization group approach (ERG) is developed for the case of pure fermionic theories by deriving a Grassmann version of the ERG equation and applying it to the study of fixed point solutions and critical exponents of the two-dimensional chiral Gross-Neveu model. An approximation based on the derivative expansion and a further truncation in the number of fields is used. Two solutions are obtained analytically in the limit $N\to \infty $, with N being the number of fermionic species. For finite N some fixed point solutions, with their anomalous dimensions and critical exponents, are computed numerically. The issue of separation of physical results from the numerous spurious ones is discussed. We argue that one of the solutions we find can be identified with that of Dashen and Frishman, whereas the others seem to be new ones.