Asymptotic safety of scalar field theories

Litim, Daniel F and Trott, Matthew J (2018) Asymptotic safety of scalar field theories. Physical Review D, 98 (12). 125006 1-24. ISSN 2470-0010

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We study 3d O(N)symmetric scalar field theories using Polchinski's renormalisation group. In the infinite N limit the model is solved exactly including at strong coupling. At short distances the theory is described by a line of asymptotically safe ultraviolet fixed points bounded by asymptotic freedom at weak, and the Bardeen-Moshe-Bander phenomenon at strong sextic coupling. The Wilson-Fisher fixed point arises as an isolated low-energy fixed point. Further results include the conformal window for asymptotic safety, convergence-limiting poles in the complex field plane, and the phase diagram with regions of first and second order phase transitions. We substantiate a duality between Polchinski's and Wetterich's versions of the functional renormalisation group, also showing that that eigenperturbations are identical at any fixed point. At a critical sextic coupling, the duality is worked out in detail to explain the spontaneous breaking of scale symmetry responsible for the generation of a light dilaton. Implications for asymptotic safety in other theories are indicated.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Physics and Astronomy
Research Centres and Groups: Theoretical Particle Physics Research Group
Subjects: Q Science
Depositing User: Alice Jackson
Date Deposited: 07 Feb 2019 11:26
Last Modified: 07 Feb 2019 11:26

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