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arXiv · 2007.12234

Renormalization-Group Behavior of $\phi^3$ Theories in $d=6$ Dimensions

John A. Gracey·Thomas A. Ryttov·Robert Shrock
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Abstract

We investigate possible renormalization-group fixed points at nonzero coupling in $\phi^3$ theories in six spacetime dimensions, using beta functions calculated to the four-loop level. We analyze three theories of this type, with (a) a one-component scalar, (b) a scalar transforming as the fundamental representation of a global ${\rm SU}(N)$ symmetry group, and (c) a scalar transforming as a bi-adjoint representation of a global ${\rm SU}(N) \otimes {\rm SU}(N)$ symmetry. We do not find robust evidence for such fixed points in theories (a) or (b). Theory (c) has the special feature that the one-loop term in the beta function is zero; implications of this are discussed.

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John A. Gracey, Thomas A. Ryttov, Robert Shrock. 2020-07-23. Renormalization-Group Behavior of $\phi^3$ Theories in $d=6$ Dimensions. https://doi.org/10.1103/physrevd.102.045016

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