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Bouwknegt / McCarthy / Pilch

The W3 Algebra

Modules, Semi-infinite Cohomology and BV Algebras
Springer Book Archives
2013. Buch. xi, 204 S.: Bibliographien. Softcover
Springer ISBN 978-3-662-14092-5
Format (B x L): 15,5 x 23,5 cm
Gewicht: 343 g
In englischer Sprache
Das Werk ist Teil der Reihe:
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.

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