Universality of Toda equation in superconformal field theories

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Title: Universality of Toda equation in superconformal field theories
Authors: Bourget, A
Rodriguez-Gomez, D
Russo, JG
Item Type: Journal Article
Abstract: We show that extremal correlators in all Lagrangian =2 superconformal field theories with a simple gauge group, when suitably defined the 𝕊4 , are governed by the same universal Toda system of equations, which dictates the structure of extremal correlators to all orders in the perturbation series. A key point is the construction of a convenient orthogonal basis for the chiral ring, by arranging towers of operators in order of increasing dimension, which has the property that the associated two-point functions satisfy decoupled Toda chain equations. We explicitly verify this in all known SCFTs based on SU(N) gauge groups as well as in superconformal QCD based on orthogonal and symplectic groups. As a by-product, we find a surprising non-renormalization property for the =2 SU(N) SCFT with one hypermultiplet in the rank-2 symmetric representation and one hypermultiplet in the rank-2 antisymmetric representation, where the two-loop terms of a large class of supersymmetric observables identically vanish.
Issue Date: 4-Feb-2019
Date of Acceptance: 27-Jan-2019
URI: http://hdl.handle.net/10044/1/73309
DOI: https://doi.org/10.1007/JHEP02(2019)011
ISSN: 1029-8479
Publisher: Springer Verlag (Germany)
Start Page: 1
End Page: 22
Journal / Book Title: The Journal of High Energy Physics
Volume: 11
Issue: 2
Copyright Statement: © The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by/4.0/), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Keywords: Science & Technology
Physical Sciences
Physics, Particles & Fields
Physics
Conformal Field Theory
Supersymmetric Gauge Theory
Science & Technology
Physical Sciences
Physics, Particles & Fields
Physics
Conformal Field Theory
Supersymmetric Gauge Theory
Nuclear & Particles Physics
01 Mathematical Sciences
02 Physical Sciences
Publication Status: Published
Open Access location: https://link.springer.com/article/10.1007/JHEP02(2019)011
Article Number: ARTN 011
Online Publication Date: 2019-02-04
Appears in Collections:Physics
Theoretical Physics



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