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Renormalization-Group Behavior of $\phi^3$ Theories in $d=6$ Dimensions
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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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Anomalous dimensions at small spins
The quadratic mass-correction combination of twist-two anomalous dimensions stays finite at small spin in the O(N) phi^4, phi^3, and Gross-Neveu-Yukawa models at the computed loop orders, enabling explicit resummations.
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