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Title: Analytic and numerical bootstrap of CFTs with $$O(m)\times O(n)$$ global symmetry in 3D

Abstract

Motivated by applications to critical phenomena and open theoretical questions, we study conformal field theories with O(m)\times O(n) O ( m ) × O ( n ) global symmetry in d=3 d = 3 spacetime dimensions. We use both analytic and numerical bootstrap techniques. Using the analytic bootstrap, we calculate anomalous dimensions and OPE coefficients as power series in \varepsilon=4-d ε = 4 d and in 1/n 1 / n , with a method that generalizes to arbitrary global symmetry. Whenever comparison is possible, our results agree with earlier results obtained with diagrammatic methods in the literature. Using the numerical bootstrap, we obtain a wide variety of operator dimension bounds, and we find several islands (isolated allowed regions) in parameter space for O(2)\times O(n) O ( 2 ) × O ( n ) theories for various values of n n . Some of these islands can be attributed to fixed points predicted by perturbative methods like the \varepsilon ε and large- n n expansions, while others appear to arise due to fixed points that have been claimed to exist in resummations of perturbative beta functions.

Authors:
 [1];  [2];  [3]
  1. University of Oxford
  2. University of Crete
  3. Los Alamos National Laboratory
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC); USDOE Laboratory Directed Research and Development (LDRD) Program; Simons Foundation
OSTI Identifier:
1659334
Alternate Identifier(s):
OSTI ID: 1711393
Report Number(s):
LA-UR-20-23147
Journal ID: ISSN 2542-4653; 035
Grant/Contract Number:  
89233218CNA000001; AC02-05CH11231; 48865; 20180709PRD1
Resource Type:
Published Article
Journal Name:
SciPost Physics Proceedings
Additional Journal Information:
Journal Name: SciPost Physics Proceedings Journal Volume: 9 Journal Issue: 3; Journal ID: ISSN 2542-4653
Publisher:
SciPost Foundation
Country of Publication:
Netherlands
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Henriksson, Johan, Kousvos, Stefanos R., and Stergiou, Andreas. Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D. Netherlands: N. p., 2020. Web. https://doi.org/10.21468/SciPostPhys.9.3.035.
Henriksson, Johan, Kousvos, Stefanos R., & Stergiou, Andreas. Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D. Netherlands. https://doi.org/10.21468/SciPostPhys.9.3.035
Henriksson, Johan, Kousvos, Stefanos R., and Stergiou, Andreas. Thu . "Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D". Netherlands. https://doi.org/10.21468/SciPostPhys.9.3.035.
@article{osti_1659334,
title = {Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D},
author = {Henriksson, Johan and Kousvos, Stefanos R. and Stergiou, Andreas},
abstractNote = {Motivated by applications to critical phenomena and open theoretical questions, we study conformal field theories with O(m)\times O(n) O ( m ) × O ( n ) global symmetry in d=3 d = 3 spacetime dimensions. We use both analytic and numerical bootstrap techniques. Using the analytic bootstrap, we calculate anomalous dimensions and OPE coefficients as power series in \varepsilon=4-d ε = 4 − d and in 1/n 1 / n , with a method that generalizes to arbitrary global symmetry. Whenever comparison is possible, our results agree with earlier results obtained with diagrammatic methods in the literature. Using the numerical bootstrap, we obtain a wide variety of operator dimension bounds, and we find several islands (isolated allowed regions) in parameter space for O(2)\times O(n) O ( 2 ) × O ( n ) theories for various values of n n . Some of these islands can be attributed to fixed points predicted by perturbative methods like the \varepsilon ε and large- n n expansions, while others appear to arise due to fixed points that have been claimed to exist in resummations of perturbative beta functions.},
doi = {10.21468/SciPostPhys.9.3.035},
journal = {SciPost Physics Proceedings},
number = 3,
volume = 9,
place = {Netherlands},
year = {2020},
month = {9}
}

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https://doi.org/10.21468/SciPostPhys.9.3.035

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