Cortes, V, Gall, L 
ORCID: 0000-0002-1805-2357 and Mohaupt, T ORCID: 0000-0002-6864-4086
(2020)
Four-dimensional vector multiplets in arbitrary signature (I).
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 17 (10).
p. 2050150.
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Abstract
We derive a necessary and sufficient condition for Poincar\'e Lie superalgebras in any dimension and signature to be isomorphic. This reduces the classification problem, up to certain discrete operations, to classifying the orbits of the Schur group on the vector space of superbrackets. We then classify four-dimensional ${\cal N}=2$ supersymmetry algebras, which are found to be unique in Euclidean and in neutral signature, while in Lorentz signature there exist two algebras with R-symmetry groups $\mathrm{U}(2)$ and $\mathrm{U(}1,1)$, respectively. By dimensional reduction we construct two off shell vector multiplet representations for each possible signature, and find that the corresponding Lagrangians always have a different relative sign between the scalar and the Maxwell term. In Lorentzian signature this is related to the existence of two non-isomorphic algebras, while in Euclidean and neutral signature the two theories are related by a local field redefinition which implements an isomorphism between the underlying supersymmetry algebras.
| Item Type: | Article |
|---|---|
| Additional Information: | 99 pages including appendices, 21 tables |
| Uncontrolled Keywords: | Poincare Lie superalgebras, extended supersymmetry, arbitrary signature |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 24 Jul 2020 07:54 |
| Last Modified: | 19 Jan 2023 00:28 |
| DOI: | 10.1142/S0219887820501509 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3053227 |
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