${\varphi }^3$ 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 $({\Delta }_{\varphi },{\Delta }_{26}^{2nd})$=$(1.6,4)$.

arXiv comment22 pages, published version

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• Seeking Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• Casimir recursion relations for general conformal blocks
• Scalar CFTs and Their Large N Limits
• Revisiting the dilatation operator of the Wilson-Fisher fixed point
• Bootstrap experiments on higher dimensional CFTs
• Inverse Bootstrapping Conformal Field Theories
• New Methods for Conformal Correlation Functions
• New method for the conformal bootstrap with OPE truncations
• Conformal Two-Point Correlation Functions from the Operator Product Expansion
• Ward-Schwinger-Dyson equations in ${\varphi }_6^3$ Quantum Field Theory
• $F_4$ symmetric ${\varphi }^3$ theory at four loops