Resonant superalgebras for supergravity

TL;DR

This paper systematically constructs and classifies a wide range of supersymmetric extensions of Poincaré and Anti-de-Sitter algebras, identifying new superalgebras suitable for supergravity models using an efficient computational method.

Contribution

It introduces a comprehensive, pattern-based computational approach to generate and classify all superalgebras with up to two supercharges, expanding beyond previous fragmentary results.

Findings

Identified 667 superalgebras, with 264 suitable for supergravity.

Provided explicit Lagrangian for one superalgebra example.

Expanded the known landscape of superalgebras relevant for supergravity.

Abstract

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 Poincar\'e 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 Poincar\'e and Anti-de Sitter ones, contain additional bosonic generators $Z_{ab}$ (Lorentz-like), and $U_a$ (translational-like) added to the standard Lorentz generator $J_{ab}$ and translation generator $P_{a}$. Our analysis includes all cases up to two fermionic supercharges, $Q_{\alpha}$ and $Y_{\alpha}$. 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 $(JP+Q)+(ZU+Y)=JPZU+QY$. 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.