Three-loop anomalous dimensions of leading-twist operators in the Gross-Neveu-Yukawa model

Abstract

We compute the anomalous dimensions of the leading-twist operators at three-loop level in the $\overline{\text{MS}}$ scheme in the Gross-Neveu-Yukawa model. Calculations are done for a number of low-spin operators using computer algebra systems, and the analytical form is reconstructed by solving a set of Diophantine equations. Calculations are optimized using the emergent supersymmetry of the corresponding generalized theory. For the obtained results, we perform a comprehensive analysis at the critical point, including a comparison with the $1/N$ expansion, a check of the generalized Gribov-Lipatov reciprocity, and an analysis of the behavior next to the rightmost singularity. The latter allows us to extract the values of Regge intercepts for all the leading-twist trajectories in the form of an $\epsilon$ expansion.