${\varphi }^3$ theory with $F_4$ flavor symmetry in $6-2\epsilon$ dimensions: 3-loop renormalization and conformal bootstrap

Abstract

We consider ${\varphi }^3$ 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 $\varphi$ 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 $\varphi$ (${\Delta }_{\varphi })$, we obtain the corresponding upper bound on the scaling dimension of the second lowest scalar primary in the $26$ representation $({\Delta }_{26}^{2nd})$ which appears in the OPE of $\varphi \times \varphi$. In $D=5.95$, we observe a sharp peak on the upper bound curve located at ${\Delta }_{\varphi }$ equal to the value predicted by the 3-loop computation. In $D=5$, we observe a weak kink on the upper bound curve at $({\Delta }_{\varphi },{\Delta }_{26}^{2nd})$=$(1.6,4)$.

22 pages, published version

References in corpus (8)

• Bootstrapping Mixed Correlators in the 3D Ising Model
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Three Loop Analysis of the Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Bootstrapping $O(N)$ Vector Models in $4<d<6$
• A Semidefinite Program Solver for the Conformal Bootstrap
• A challenge to the $a$-theorem in six dimensions
• Conformal Bootstrap Approach to O(N) Fixed Points in Five Dimensions

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