A nilpotency index of conformal manifolds

A nilpotency index of conformal manifolds

Abstract We show that exactly marginal operators of Supersymmetric Conformal Field Theories (SCFTs) with four supercharges cannot obtain a vacuum expectation value at a generic point on the conformal manifold. Exactly marginal operators are therefore nilpotent in the chiral ring. This allows us to a...

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Main Authors: Zohar Komargodski, Shlomo S. Razamat, Orr Sela, Adar Sharon
Format: Article
Language:English
Published: SpringerOpen 2020-10-01
Series:Journal of High Energy Physics
Subjects:
Conformal Field Theory
Supersymmetric Gauge Theory
Online Access:http://link.springer.com/article/10.1007/JHEP10(2020)183
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spelling doaj-56f0104ae7dd46faa48affd077b4e8ec2020-11-25T03:44:32ZengSpringerOpenJournal of High Energy Physics1029-84792020-10-0120201012110.1007/JHEP10(2020)183A nilpotency index of conformal manifoldsZohar Komargodski0Shlomo S. Razamat1Orr Sela2Adar Sharon3Simons Center for Geometry and PhysicsDepartment of Physics, TechnionDepartment of Physics, TechnionDepartment of Particle Physics and Astrophysics, Weizmann Institute of ScienceAbstract We show that exactly marginal operators of Supersymmetric Conformal Field Theories (SCFTs) with four supercharges cannot obtain a vacuum expectation value at a generic point on the conformal manifold. Exactly marginal operators are therefore nilpotent in the chiral ring. This allows us to associate an integer to the conformal manifold, which we call the nilpotency index of the conformal manifold. We discuss several examples in diverse dimensions where we demonstrate these facts and compute the nilpotency index.http://link.springer.com/article/10.1007/JHEP10(2020)183Conformal Field TheorySupersymmetric Gauge Theory
collection DOAJ
language English
format Article
sources DOAJ
author Zohar Komargodski
Shlomo S. Razamat
Orr Sela
Adar Sharon
spellingShingle Zohar Komargodski
Shlomo S. Razamat
Orr Sela
Adar Sharon
A nilpotency index of conformal manifolds
Journal of High Energy Physics
Conformal Field Theory
Supersymmetric Gauge Theory
author_facet Zohar Komargodski
Shlomo S. Razamat
Orr Sela
Adar Sharon
author_sort Zohar Komargodski
title A nilpotency index of conformal manifolds
title_short A nilpotency index of conformal manifolds
title_full A nilpotency index of conformal manifolds
title_fullStr A nilpotency index of conformal manifolds
title_full_unstemmed A nilpotency index of conformal manifolds
title_sort nilpotency index of conformal manifolds
publisher SpringerOpen
series Journal of High Energy Physics
issn 1029-8479
publishDate 2020-10-01
description Abstract We show that exactly marginal operators of Supersymmetric Conformal Field Theories (SCFTs) with four supercharges cannot obtain a vacuum expectation value at a generic point on the conformal manifold. Exactly marginal operators are therefore nilpotent in the chiral ring. This allows us to associate an integer to the conformal manifold, which we call the nilpotency index of the conformal manifold. We discuss several examples in diverse dimensions where we demonstrate these facts and compute the nilpotency index.
topic Conformal Field Theory
Supersymmetric Gauge Theory
url http://link.springer.com/article/10.1007/JHEP10(2020)183
work_keys_str_mv AT zoharkomargodski anilpotencyindexofconformalmanifolds
AT shlomosrazamat anilpotencyindexofconformalmanifolds
AT orrsela anilpotencyindexofconformalmanifolds
AT adarsharon anilpotencyindexofconformalmanifolds
AT zoharkomargodski nilpotencyindexofconformalmanifolds
AT shlomosrazamat nilpotencyindexofconformalmanifolds
AT orrsela nilpotencyindexofconformalmanifolds
AT adarsharon nilpotencyindexofconformalmanifolds
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