ϕ 3 theory with F 4 flavor symmetry in 6 − 2 ϵ dimensions: 3-loop renormalization and conformal bootstrap

We consider ϕ 3 theory in 6 − 2ϵ 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 ϕ are also computed. we then employ conformal bootstrap technique to study the fixed point predicted from the perturbative approach. for each putative scaling dimension of ϕ (δ ϕ ), we obtain the corresponding upper bound on the scaling dimension of the second lowest scalar primary in the 26 representation (δ 2nd ) which appears in the ope of ϕ × ϕ. in d = 5.95, we observe a sharp peak on the upper bound curve located at δ ϕ equal to the value predicted by the 3-loop computation. in d = 5, we observe a weak kink on the upper bound curve at (δ ϕ , δ 2nd ) = (1.6, 4).