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Asymptotic safety of scalar field theories

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journal contribution
posted on 2023-06-09, 16:47 authored by Daniel LitimDaniel Litim, Matthew J Trott
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.

History

Publication status

  • Published

File Version

  • Published version

Journal

Physical Review D

ISSN

2470-0010

Publisher

American Physical Society

Issue

12

Volume

98

Page range

125006 1-24

Department affiliated with

  • Physics and Astronomy Publications

Research groups affiliated with

  • Theoretical Particle Physics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2019-02-07

First Open Access (FOA) Date

2019-02-07

First Compliant Deposit (FCD) Date

2019-02-06

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