Renormalization-Group Behavior of φ3 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 φ3 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 SU(N) symmetry group, and (c) a scalar transforming as a bi-adjoint representation of a global SU(N) ⊗ 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.
Original languageEnglish
Article number045016
JournalPhysical Review D. Particles and fields
Volume102
Issue number4
Number of pages9
ISSN2470-0010
DOIs
Publication statusPublished - 24. Aug 2020

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