Homological classification of topological terms in sigma models on homogeneous spaces
View / Open Files
Publication Date
2018Journal 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.
Keywords
Effective Field Theories, Sigma Models, Topological Field Theories
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
Statistics
Total file downloads (since January 2020). For more information on metrics see the
IRUS guide.
Recommended or similar items
The current recommendation prototype on the Apollo Repository will be turned off on 03 February 2023. Although the pilot has been fruitful for both parties, the service provider IKVA is focusing on horizon scanning products and so the recommender service can no longer be supported. We recognise the importance of recommender services in supporting research discovery and are evaluating offerings from other service providers. If you would like to offer feedback on this decision please contact us on: support@repository.cam.ac.uk