Solving the Conformal Bootstrap: Four-Fermion Interactions at 2<d<4

TL;DR

This paper develops a conformal bootstrap method for four-fermion theories in dimensions between 2 and 4, providing analytical results for critical exponents and anomalous dimensions at strong coupling.

Contribution

It introduces a bootstrap approach to four-fermion theories at strong coupling and computes anomalous dimensions to order 1/N^2 in a five-vertex approximation.

Findings

Derived anomalous dimensions of fermion and composite operators to order 1/N^2.

Provided a simplified method for calculating next-to-leading order corrections.

Solved bootstrap equations in the five-vertex approximation for the specified theories.

Abstract

We formulate the conformal bootstrap approach to four--fermion theory at its strong coupling fixed point in dimensions $2<d<4$. We present a solution of the bootstrap equations in the five--vertex approximation. We show that the bootstrap approach gives a particularly simple way to obtain next to leading order corrections to critical exponents in the large $N$ expansion and present the values of the anomalous dimensions of the fermion field $\psi$ and the composite $\bar\psi\psi$ to order $1/N^2$.