https://doi.org/10.1140/epjc/s10052-022-10156-9
Regular Article - Theoretical Physics
Resonant superalgebras for supergravity
Institute for Theoretical Physics, University of Wrocław, pl. M. Borna 9, 50-204, Wrocław, Poland
Received:
5
November
2021
Accepted:
20
February
2022
Published online:
24
March
2022
Considering supergravity theory is a natural step in the development of gravity models. This paper follows the “algebraic“ path and constructs possible extensions of the Poincaré and Anti-de-Sitter algebras, which inherit their basic commutation structure. Previously achieved results of this type are fragmentary and show only a limited fraction of possible algebraic realizations. Our paper presents the newly obtained symmetry algebras, evaluated within an efficient pattern-based computational method of generating the so-called ‘resonating’ algebraic structures. These supersymmetric extensions of algebras, going beyond the Poincaré and Anti-de Sitter ones, contain additional bosonic generators 
(Lorentz-like), and 
(translational-like) added to the standard Lorentz generator 
and translation generator 
. Our analysis includes all cases up to two fermionic supercharges, 
and 
. The delivered plethora of superalgebras includes few past results and offers a vastness of new examples. The list of the cases is complete and contains all superalgebras up to two of Lorentz-like, translation-like, and supercharge-like generators 
. In the latter class, among 667 founded superalgebras, the 264 are suitable for direct supergravity construction. For each of them, one can construct a unique supergravity model defined by the Lagrangian. As an example, we consider one of the algebra configurations and provide its Lagrangian realization.
© The Author(s) 2022. corrected publication 2022
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