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Counting RG flows

Gukov, Sergei (2016) Counting RG flows. Journal of High Energy Physics, 2016 (1). Art. No. 020. ISSN 1126-6708. doi:10.1007/JHEP01(2016)020.

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Interpreting renormalization group flows as solitons interpolating between different fixed points, we ask various questions that are normally asked in soliton physics but not in renormalization theory. Can one count RG flows? Are there different “topological sectors” for RG flows? What is the moduli space of an RG flow, and how does it compare to familiar moduli spaces of (supersymmetric) dowain walls? Analyzing these questions in a wide variety of contexts — from counting RG walls to AdS/CFT correspondence — will not only provide favorable answers, but will also lead us to a unified general framework that is powerful enough to account for peculiar RG flows and predict new physical phenomena. Namely, using Bott’s version of Morse theory we relate the topology of conformal manifolds to certain properties of RG flows that can be used as precise diagnostics and “topological obstructions” for the strong form of the C-theorem in any dimension. Moreover, this framework suggests a precise mechanism for how the violation of the strong C-theorem happens and predicts “phase transitions” along the RG flow when the topological obstruction is non-trivial. Along the way, we also find new conformal manifolds in well-known 4d CFT’s and point out connections with the superconformal index and classifying spaces of global symmetry groups.

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Gukov, Sergei0000-0002-9486-1762
Additional Information:© 2016 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 SCOAP3. Received: September 2, 2015; Accepted: December 20, 2015; Published: January 5, 2016. I would like to thank N. Deger, L. Dixon, K. Intriligator, V. Lysov, Yu Nakayama, H. Ooguri, L. Rastelli, D. Roggenkamp, E. Sezgin, A. Shapere, M. Strassler, R. Sundrum, D. Xie, and W. Yan for useful discussions and comments. It is also a pleasure to thank the organizers and participants of the conference "Progress and Application of Modern QFT" in Aspen Feb. 16-21, 2015, where I had the opportunity to discuss the results presented here. This work is funded by the DOE Grant DE-SC0011632 and the Walter Burke Institute for Theoretical Physics.
Group:Walter Burke Institute for Theoretical Physics
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Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Subject Keywords:Supersymmetric gauge theory, Renormalization Group
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Issue or Number:1
Record Number:CaltechAUTHORS:20150311-193040484
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55717
Deposited By: Joy Painter
Deposited On:12 Mar 2015 04:07
Last Modified:10 Nov 2021 20:49

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