Homological classification of topological terms in sigma models on homogeneous spaces
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Publication Date
2018-09-26Journal Title
Journal of High Energy Physics
ISSN
1126-6708
Publisher
Springer Science and Business Media LLC
Volume
2018
Issue
9
Type
Article
Metadata
Show full item recordCitation
Davighi, J., & Gripaios, B. (2018). Homological classification of topological terms in sigma models on homogeneous spaces. Journal of High Energy Physics, 2018 (9) https://doi.org/10.1007/JHEP09(2018)155
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
$H \subset G$). 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.
Sponsorship
Science and Technology Facilities Council (ST/P000681/1)
Identifiers
External DOI: https://doi.org/10.1007/JHEP09(2018)155
This record's URL: https://www.repository.cam.ac.uk/handle/1810/285538
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