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Critical $O(2)$ and $O(3)$ $\phi^4$ theories near six dimensions · Around

2015

Critical $O(2)$ and $O(3)$ $\phi^4$ theories near six dimensions

Herbut, Igor F., Janssen, Lukas

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We consider $O(N)$-symmetric bosonic $\phi^4$ field theories above four dimensions, and propose a new reformulation in terms of an irreducible tensorial field with a cubic and Yukawa terms.

The $\phi^4$ field theory so rewritten exhibits real and nontrivial IR-stable fixed points near and below six dimension, for low values of $N$ such as $N=2$ and $N=3$.
The so-defined UV completions of the $O(2)$ and $O(3)$ models hence constitute precious examples of asymptotically safe quantum field theories.
The possibility of an extension of our results to five dimensions is discussed.

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