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Perturbative search for dead end CFTs

Nakayama, Yu (2015) Perturbative search for dead end CFTs. Journal of High Energy Physics, 2015 (5). Art. No. 46. ISSN 1126-6708. doi:10.1007/JHEP05(2015)046.

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To explore the possibility of self-organized criticality, we look for CFTs without any relevant scalar deformations (a.k.a. dead-end CFTs) within power-counting renormalizable quantum field theories with a weakly coupled Lagrangian description. In three dimensions, the only candidates are pure (Abelian) gauge theories, which may be further deformed by Chern-Simons terms. In four dimensions, we show that there are infinitely many non-trivial candidates based on chiral gauge theories. Using the three-loop beta functions, we compute the gap of scaling dimensions above the marginal value, and it can be as small as O(10^(-5)) and robust against the perturbative corrections. These classes of candidates are very weakly coupled and our perturbative conclusion seems difficult to refute. Thus, the hypothesis that non-trivial dead-end CFTs do not exist is likely to be false in four dimensions.

Item Type:Article
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URLURL TypeDescription Paper
Nakayama, Yu0000-0002-1747-5147
Additional Information:© 2015 the Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP. Received: February 2, 2015; Revised: March 25, 2015; Accepted: April 21, 2015; Published: May 8, 2015. The author would like to thank the organizers of two wonderful workshops “Conformal Field Theories in Higher Dimensions (Back to the Bootstrap 3)” at CERN and “Higher Spin Symmetries and Conformal Bootstrap” at Princeton for stimulating atmospheres where he got gradually convinced to write up the material discussed here. He would like to thank Elias Kiritsis, Luminita Mihaila and Slava Rychkov for correspondence and discussions. He also acknowledges John Schwarz for careful reading of the manuscript. This work is supported by a Sherman Fairchild Senior Research Fellowship at the California Institute of Technology and DOE grant number DE-SC0011632.
Group:Walter Burke Institute for Theoretical Physics
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Sherman Fairchild FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Subject Keywords: Conformal and W Symmetry Renormalization Group
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Issue or Number:5
Record Number:CaltechAUTHORS:20150316-141432264
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Official Citation:Perturbative search for dead-end CFTs Yu Nakayama Article 46
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55806
Deposited By: Joy Painter
Deposited On:16 Mar 2015 21:27
Last Modified:10 Nov 2021 20:50

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