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Title: Bootstrapping SCFTs with four supercharges

Abstract

Here, we study the constraints imposed by superconformal symmetry, crossing symmetry, and unitarity for theories with four supercharges in spacetime dimension 2 ≤ d ≤ 4. We show how superconformal algebras with four Poincaré supercharges can be treated in a formalism applicable to any, in principle continuous, value of d and use this to construct the superconformal blocks for any d ≤ 4. We then use numerical bootstrap techniques to derive upper bounds on the conformal dimension of the first unprotected operator appearing in the OPE of a chiral and an anti-chiral superconformal primary. We obtain an intriguing structure of three distinct kinks. We argue that one of the kinks smoothly interpolates between the d = 2, N=(2,2) minimal model with central charge c = 1 and the theory of a free chiral multiplet in d = 4, passing through the critical Wess-Zumino model with cubic superpotential in intermediate dimensions.

Authors:
 [1];  [2];  [3];  [4]
+ Show Author Affiliations
  1. Katholieke Univ. Leuven, (Belgium). Inst. for Theoretical Physics
  2. European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theory Division; Paris-Sorbonne and Pierre-and-Marie Curie (UPMC) Univ., CNRS, UMR, Paris (France). Lab. of Theoretical and High Energy Physics (LPTHE)
  3. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
  4. European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theory Division
Publication Date:
Research Org.:
European Organization for Nuclear Research (CERN), Geneva (Switzerland); Brown Univ., Providence, RI (United States)
Sponsoring Org.:
USDOE; European Science Foundation (ESF); European Union (EU)
OSTI Identifier:
1454592
Grant/Contract Number:  
SC0010010; BOF/STG/14/032; PIEF-GA-2013-623606
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 8; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Supersymmetric gauge theory; Field Theories in Lower Dimensions; Conformal and W Symmetry

Citation Formats

Bobev, Nikolay, El-Showk, Sheer, Mazac, Dalimil, and Paulos, Miguel F. Bootstrapping SCFTs with four supercharges. United States: N. p., 2015. Web. doi:10.1007/JHEP08(2015)142.
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Bobev, Nikolay, El-Showk, Sheer, Mazac, Dalimil, & Paulos, Miguel F. Bootstrapping SCFTs with four supercharges. United States. https://doi.org/10.1007/JHEP08(2015)142
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Bobev, Nikolay, El-Showk, Sheer, Mazac, Dalimil, and Paulos, Miguel F. Thu . "Bootstrapping SCFTs with four supercharges". United States. https://doi.org/10.1007/JHEP08(2015)142. https://www.osti.gov/servlets/purl/1454592.
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@article{osti_1454592,
title = {Bootstrapping SCFTs with four supercharges},
author = {Bobev, Nikolay and El-Showk, Sheer and Mazac, Dalimil and Paulos, Miguel F.},
abstractNote = {Here, we study the constraints imposed by superconformal symmetry, crossing symmetry, and unitarity for theories with four supercharges in spacetime dimension 2 ≤ d ≤ 4. We show how superconformal algebras with four Poincaré supercharges can be treated in a formalism applicable to any, in principle continuous, value of d and use this to construct the superconformal blocks for any d ≤ 4. We then use numerical bootstrap techniques to derive upper bounds on the conformal dimension of the first unprotected operator appearing in the OPE of a chiral and an anti-chiral superconformal primary. We obtain an intriguing structure of three distinct kinks. We argue that one of the kinks smoothly interpolates between the d = 2, N=(2,2) minimal model with central charge c = 1 and the theory of a free chiral multiplet in d = 4, passing through the critical Wess-Zumino model with cubic superpotential in intermediate dimensions.},
doi = {10.1007/JHEP08(2015)142},
journal = {Journal of High Energy Physics (Online)},
number = 8,
volume = 2015,
place = {United States},
year = {Thu Aug 27 00:00:00 EDT 2015},
month = {Thu Aug 27 00:00:00 EDT 2015}
}
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https://doi.org/10.1007/JHEP08(2015)142
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    Works referencing / citing this record:

    Scaling and superscaling solutions from the functional renormalization group
    journal, October 2015

    Quantum integrable systems from conformal blocks
    journal, May 2017

    Critical Wess-Zumino models with four supercharges in the functional renormalization group approach
    journal, November 2018

    Critical Wess-Zumino models with four supercharges in the functional renormalization group approach
    other, January 2018

    • Feldmann, Polina; Wipf, Andreas; Zambelli, Luca
    • College Park : American Physical Society (APS)
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    On the CFT operator spectrum at large global charge
    text, January 2015

    Superintegrability of $d$-Dimensional Conformal Blocks
    text, January 2016

    Scaling and superscaling solutions from the functional renormalization group
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    Superintegrability of $d$-dimensional Conformal Blocks
    text, January 2016

    Quantum Integrable Systems from Conformal Blocks
    text, January 2016

    The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
    text, January 2018

    Landscape of Simple Superconformal Field Theories in 4d
    text, January 2018

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