The Analytic Bootstrap in Fermionic CFTs

TL;DR

This work develops an analytic bootstrap for fermionic CFTs with weakly broken higher-spin symmetry, using twist-conformal blocks and crossing symmetry to extract CFT data perturbatively in ε. By studying four-point functions of composite fermionic operators in the Gross-Neveu and Gross-Neveu–Yukawa models, the authors reproduce known bilinear anomalous dimensions, uncover new OPE-coefficient corrections, and determine quadrilinear operator data, including their degeneracies. They emphasize the role of finite- and infinite-spin sectors, global U(N_f) representations, and the mixing of singlet and adjoint currents, while also addressing a nontrivial 2D-like solution where the fundamental fermion is not in the spectrum. Overall, the approach yields a coherent, spin-summed picture of operator dimensions and OPEs across two perturbative windows, offering new analytic benchmarks for fermionic CFTs at criticality.

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.