Asymptotic safety of scalar field theories
Abstract
We study 3d O(N) symmetric scalar field theories using Polchinski’s renormalization 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 renormalization group, also showing 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.
Citation
Litim , D F & Trott , M J 2018 , ' Asymptotic safety of scalar field theories ' , Physical Review D - Particles, Fields, Gravitation and Cosmology , vol. 98 , no. 12 , 125006 . https://doi.org/10.1103/PhysRevD.98.125006
Publication
Physical Review D - Particles, Fields, Gravitation and Cosmology
Status
Peer reviewed
ISSN
1550-7998Type
Journal article
Description
Part of this work was performed at the Aspen Center for Physics, which is supported by National Science Foundation Grant No. PHY-1607611. D. L. gratefully acknowledges financial support by the Simons Foundation. M. J. T. acknowledges financial support from the CM-CDT under Engineering and Physical Sciences Research Council (UK) Grant No. EP/L015110/1.Collections
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