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Asymptotic safety of scalar field theories
journal contribution
posted on 2023-06-09, 16:47 authored by Daniel LitimDaniel Litim, Matthew J TrottWe 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.
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Publication status
- Published
File Version
- Published version
Journal
Physical Review DISSN
2470-0010Publisher
American Physical SocietyExternal DOI
Issue
12Volume
98Page range
125006 1-24Department 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
2019-02-07First Open Access (FOA) Date
2019-02-07First Compliant Deposit (FCD) Date
2019-02-06Usage metrics
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