φ3 theory with F4 flavor symmetry in 6-2ε dimensions: 3-loop renormalization and conformal bootstrap

We consider phi(3) theory in 6 - 2 epsilon with F-4 global symmetry. The beta function is calculated up to 3 loops, and a stable unitary IR fixed point is observed. The anomalous dimensions of operators quadratic or cubic in phi are also computed. We then employ conformal bootstrap technique to study the fi xed point predicted from the perturbative approach. For each putative scaling dimension of phi (Delta(phi)), we obtain the corresponding upper bound on the scaling dimension of the second lowest scalar primary in the 26 representation (Delta(2nd)(26)) which appears in the OPE of phi x phi. In D = 5.95, we observe a sharp peak on the upper bound curve located at Delta(phi) equal to the value predicted by the 3-loop computation. In D = 5, we observe a weak kink on the upper bound curve at (Delta(phi), Delta(2nd)(26)) = (1.6, 4).