The Analytic Bootstrap in Fermionic CFTs

TL;DR

This paper uses the large spin bootstrap method to analyze fermionic conformal field theories, deriving anomalous dimensions and OPE coefficients in models near critical dimensions, and discovering new solutions in fermionic theories.

Contribution

It applies the large spin bootstrap to fermionic CFTs, providing perturbative results for operator dimensions and OPE coefficients, including new solutions where the fundamental field is absent.

Findings

Derived anomalous dimensions and OPE coefficients for Gross-Neveu models.

Found a non-trivial fermionic solution in 2+ε dimensions without the fundamental field.

Results are valid to all orders in spin and reproduce known data.

Abstract

We apply the method of the large spin bootstrap to analyse fermionic conformal field theories with weakly broken higher spin symmetry. Through the study of correlators of composite operators, we find the anomalous dimensions and OPE coefficients in the Gross-Neveu model in $d=2+\varepsilon$ dimensions and the Gross-Neveu-Yukawa model in $d=4-\varepsilon$ dimensions, based only on crossing symmetry. Furthermore a non-trivial solution in the $d=2+\varepsilon$ expansion is found for a fermionic theory in which the fundamental field is not part of the spectrum. The results are perturbative in $\varepsilon$ and valid to all orders in the spin, reproducing known results for operator dimensions and providing some new results for operator dimensions and OPE coefficients.