Resonant superalgebras for supergravity

Abstract

AbstractConsidering 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 $$Z_{ab}$$ Z ab (Lorentz-like), and $$U_a$$ U a (translational-like) added to the standard Lorentz generator $$J_{ab}$$ J ab and translation generator $$P_{a}$$ P a . Our analysis includes all cases up to two fermionic supercharges, $$Q_{\alpha }$$ Q α and $$Y_{\alpha }$$ Y α . 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 $$(JP+Q)+(ZU+Y)=JPZU+QY$$ ( J P + Q ) + ( Z U + Y ) = J P Z U + Q Y . 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.