On the Hidden Maxwell Superalgebra underlying D=4 Supergravity

Abstract

In this work, we expand the hidden $AdS$-Lorentz superalgebra underlying $D=4$ supergravity, reaching a (hidden) Maxwell superalgebra. The latter can be viewed as an extension involving cosmological constant of the superalgebra underlying $D=4$ supergravity in flat spacetime. We write the Maurer-Cartan equations in this context and we find some interesting extensions of the antisymmetric $3$-form $A^{(3)}$ appearing in the Free Differential Algebra in Minkowski space. The structure of Free Differential Algebras is obtained by considering the zero curvature equations. We write the parametrization of $A^{(3)}$ in terms of $1$-forms and we rend the topological features of its extensions manifest. We interestingly find out that the structure of these extensions, and consequently the structure of the corresponding boundary contribution $d{A}^{(3)}$, strongly depends on the form of the extra fermionic generator appearing in the hidden Maxwell superalgebra. The model we develop in this work is defined in an enlarged superspace with respect to the ordinary one, and the extra bosonic and fermionic $1$-forms required for the closure of the hidden Maxwell superalgebra must be considered as physical fields in this enlarged superspace.

26 pages, Erratum of the previous version. Accepted for publication in Fortschritte der Physik, Version of Record online: 21 JUN 2017

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• Three-dimensional Maxwellian extended Bargmann supergravity
• Generalized Pure Lovelock Gravity
• $\mathcal{N}$-extended Maxwell supergravities as Chern-Simons theories in three spacetime dimensions
• Galilean free Lie algebras
• Three-dimensional exotic Newtonian gravity with cosmological constant
• On the supersymmetry invariance of flat supergravity with boundary
• Three-dimensional Poincaré supergravity and $\mathcal{N}$-extended supersymmetric BMS${}_3$ algebra
• On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions
• Three-dimensional exotic Newtonian supergravity theory with cosmological constant
• Three-dimensional Maxwellian Extended Newtonian gravity and flat limit
• Generalized cosmological term in D=4 supergravity from a new AdS-Lorentz superalgebra
• Generalized AdS-Lorentz deformed supergravity on a manifold with boundary
• The Maxwell group in 2+1 dimensions and its infinite-dimensional enhancements
• Hypersymmetric extensions of Maxwell Chern-Simons gravity in (2+1) dimensions
• Symmetries of M-theory and free Lie superalgebras
• $D=4$ supergravity from the Maxwell-Weyl superalgebra
• Resonant superalgebras and $\mathcal{N}=1$ supergravity theories in three spacetime dimensions
• Off-shell supersymmetry via manifest invariance
• Supergravities and Branes from Hilbert-Poincaré Series
• Non-Lorentzian Supergravity and Kinematical Superalgebras
• On the role of torsion and higher forms in off-shell supergravity
• Hietarinta Chern-Simons supergravity and its asymptotic structure
• Asymptotic structure of three-dimensional Maxwell Chern-Simons gravity coupled to spin-3 fields
• Three-dimensional Maxwellian Carroll gravity theory and the cosmological constant
• On the geometric approach to the boundary problem in supergravity