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Journal of High Energy Physics

, 2018:155 | Cite as

Homological classification of topological terms in sigma models on homogeneous spaces

  • Joe DavighiEmail author
  • Ben Gripaios
Open Access
Regular Article - Theoretical Physics

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.

Keywords

Effective Field Theories Sigma Models Topological Field Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeU.K.
  2. 2.Cavendish LaboratoryUniversity of CambridgeCambridgeU.K.

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