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Homological classification of topological terms in sigma models on homogeneous spaces

Published version
Peer-reviewed

Type

Article

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Authors

Gripaios, B 

Abstract

We classify the topological terms (in a sense to be made precise) that may appear in a non-linear sigma model based on maps from an arbitrary worldvolume manifold to a homogeneous space G/H (where G is an arbitrary Lie group and HG). We derive a new condition for G-invariance of topological terms, which is necessary and sufficient (at least when G is connected), and discuss a variety of examples in quantum mechanics and quantum field theory. In the present work we discuss only terms that may be written in terms of (possibly only locally-defined) differential forms on G/H, leading to an action that is manifestly local. Such terms come in one of two types, with prototypical quantum-mechanical examples given by the Aharonov-Bohm effect and the Dirac monopole. The classification is based on the observation that, for topological terms, the maps from the worldvolume to G/H may be replaced by singular homology cycles on G/H. In a forthcoming paper we apply the results to phenomenological models in which the Higgs boson is composite.

Description

Keywords

Effective Field Theories, Sigma Models, Topological Field Theories

Journal Title

Journal of High Energy Physics

Conference Name

Journal ISSN

1126-6708
1029-8479

Volume Title

2018

Publisher

Springer Science and Business Media LLC
Sponsorship
Science and Technology Facilities Council (ST/P000681/1)