phi(3) theory with F4 flavor symmetry in 6-2 epsilon dimensions: 3-loop renormalization and conformal bootstrap

Abstract

We consider 3 theory in 6 2 with F4 global symmetry. The beta function is calculated up to 3 loops, and a stable unitary IR xed point is observed. The anomalous dimensions of operators quadratic or cubic in are also computed. We then employ conformal bootstrap technique to study the xed point predicted from the perturbative approach. For each putative scaling dimension of (), we obtain the corresponding upper bound on the scaling dimension of the second lowest scalar primary in the 26 representation (2nd 26 ) which appears in the OPE of . In D = 5:95, we observe a sharp peak on the upper bound curve located at equal to the value predicted by the 3-loop computation. In D = 5, we observe a weak kink on the upper bound curve at (;2nd 26 ) = (1:6; 4). (c) The Authors.