The W3 Algebra: Modules, Semi-infinite Cohomology and BV Algebras by Peter BouwknegtThe W3 Algebra: Modules, Semi-infinite Cohomology and BV Algebras by Peter Bouwknegt

The W3 Algebra: Modules, Semi-infinite Cohomology and BV Algebras

byPeter Bouwknegt, Jim Mccarthy, Krzysztof Pilch

Paperback | November 13, 2013

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The study of W algebras began in 1985 in the context of two-dimensional conf- mal field theories, the aim being to explore higher-spin extensions of the Virasoro algebra. Given the simultaneous growth in the understanding of two-dimensional metric gravity inspired by analyses of string models, it was inevitable that these algebras would be applied to give analogues of putative higher-spin gravity t- ories. This book is an exposition of the past few years of our work on such an application for the algebra: in particular, the BRST quantization of the n- critical 4D string. We calculate the physical spectrum as a problem in BRST cohomology. The corresponding operator cohomology forms a BV algebra, for which we provide a geometrical model. The algebra has one further generator, of spin three, in addition to the (spin two) energy-momentum tensor which generates the Virasoro algebra. C- trary to the Virasoro algebra, it is an algebra defined by nonlinear relations. In deriving our understanding of the resulting gravity theories we have had to - velop a number of results on the representation theory of W algebras, to replace the standard techniques that were so successful in treating linear algebras.
Title:The W3 Algebra: Modules, Semi-infinite Cohomology and BV AlgebrasFormat:PaperbackDimensions:204 pages, 23.5 × 15.5 × 0.07 inPublished:November 13, 2013Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3662140926

ISBN - 13:9783662140925

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Table of Contents

and Preliminaries.- W Algebras and Their Modules.- BRST Cohomology of the 4D W3 String.- Batalin-Vilkovisky Algebras.- The BV Algebra of the W3 String.