W algebras are L∞ algebras

A bstract It is shown that the closure of the infinitesimal symmetry transformations underlying classical W algebras give rise to L ∞ algebras with in general field dependent gauge parameters. Therefore, the class of well understood W algebras provides highly nontrivial examples of such strong homot...

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Bibliographic Details
Published inThe journal of high energy physics Vol. 2017; no. 7
Main Authors Blumenhagen, Ralph, Fuchs, Michael, Traube, Matthias
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 12.07.2017
Subjects
Classical and Quantum Gravitation
Elementary Particles
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Conformal and W Symmetry
Conformal Field Models in String Theory
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Summary:A bstract It is shown that the closure of the infinitesimal symmetry transformations underlying classical W algebras give rise to L ∞ algebras with in general field dependent gauge parameters. Therefore, the class of well understood W algebras provides highly nontrivial examples of such strong homotopy Lie algebras. We develop the general formalism for this correspondence and apply it explicitly to the classical W 3 algebra.
ISSN:1029-8479
DOI:10.1007/JHEP07(2017)060