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The W3 Algebra

Modules, Semi-infinite Cohomology and BV Algebras

  • Book
  • © 1996

Overview

Authors:
  1. Peter Bouwknegt

    1. Department of Physics and Mathematical Physics, University of Adelaide, Adelaide, Australia

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  2. Jim McCarthy

    1. Department of Physics and Mathematical Physics, University of Adelaide, Adelaide, Australia

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    You can also search for this author in PubMed   Google Scholar

  3. Krzysztof Pilch

    1. Department of Physics and Astronomy, University of Southern California, Los Angeles, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Physics Monographs (LNPMGR, volume 42)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-XI
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  2. Introduction and Preliminaries

    Pages 1-16

  3. W Algebras and Their Modules

    Pages 17-52

  4. BRST Cohomology of the 4D W3 String

    Pages 53-77

  5. Batalin-Vilkovisky Algebras

    Pages 79-123

  6. The BV Algebra of the W3 String

    Pages 125-148

  7. Back Matter

    Pages 149-204
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Physics and Mathematical Physics, University of Adelaide, Adelaide, Australia

    Peter Bouwknegt, Jim McCarthy

  • Department of Physics and Astronomy, University of Southern California, Los Angeles, USA

    Krzysztof Pilch

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