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LOOP GROUPS, STRING CLASSES AND EQUIVARIANT COHOMOLOGY

Part of: Quantum field theory; related classical field theories Differential topology Fiber spaces and bundles

Published online by Cambridge University Press:  22 March 2011

RAYMOND F. VOZZO
RAYMOND F. VOZZO*
Affiliation:
School of Mathematical Sciences, University of Adelaide, Adelaide SA 5005, Australia (email: raymond.vozzo@adelaide.edu.au)
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Abstract

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We give a classifying theory for LG-bundles, where LG is the loop group of a compact Lie group G, and present a calculation for the string class of the universal LG-bundle. We show that this class is in fact an equivariant cohomology class and give an equivariant differential form representing it. We then use the caloron correspondence to define (higher) characteristic classes for LG-bundles and to prove a result for characteristic classes for based loop groups for the free loop group. These classes have a natural interpretation in equivariant cohomology and we give equivariant differential form representatives for the universal case in all odd dimensions.

Keywords

loop groupsstring classcaloron correspondenceequivariant cohomology

MSC classification

Secondary: 55R10: Fiber bundles 57R20: Characteristic classes and numbers 81T30: String and superstring theories; other extended objects (e.g., branes)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 90 , Issue 1 , February 2011 , pp. 109 - 127
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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