The analytic bootstrap infermionic CFTs

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 + epsilon dimensions and the Gross-Neveu-Yukawa model in d = 4 - epsilon dimensions, based only on crossing symmetry. Furthermore a non-trivial solution in the d = 2 + epsilon expansion is found for a fermionic theory in which the fundamental field is not part of the spectrum. The results are perturbative in epsilon 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.