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Asymptotic safety of scalar field theories

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Litim_2018_PRD_Asymptotic_CC.pdf (1.576Mb)
Date
12/12/2018
Author
Litim, Daniel F.
Trott, Matthew J.
Funder
EPSRC
Grant ID
EP/L015110/1
Keywords
QC Physics
T-NDAS
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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
DOI
https://doi.org/10.1103/PhysRevD.98.125006
ISSN
1550-7998
Type
Journal article
Rights
Copyright © 2018 The Author(s). Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
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.
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  • University of St Andrews Research
URL
https://arxiv.org/abs/1810.01678
URI
http://hdl.handle.net/10023/16877

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