Minimal D=4 supergravity from the superMaxwell algebra

Abstract

We show that the first-order D=4, N=1 pure supergravity lagrangian four-form can be obtained geometrically as a quadratic expression in the curvatures of the Maxwell superalgebra. This is achieved by noticing that the relative coefficient between the two terms of the Lagrangian that makes the action locally supersymmetric also determines trivial field equations for the gauge fields associated with the extra generators of the Maxwell superalgebra. Along the way, a convenient geometric procedure to check the local supersymmetry of a class of lagrangians is developed.

Plain latex, 14 pages. Two misprints corrected, one reference added

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• Three-dimensional Maxwellian extended Bargmann supergravity
• $\mathcal{N}$-extended Maxwell supergravities as Chern-Simons theories in three spacetime dimensions
• Generalized supersymmetric cosmological term in N=1 Supergravity
• Three-dimensional exotic Newtonian gravity with cosmological constant
• On the supersymmetry invariance of flat supergravity with boundary
• On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions
• $D=4$ topological gravity from gauging the Maxwell-special-affine group
• Maxwell-affine gauge theory of gravity
• Generalized cosmological term in D=4 supergravity from a new AdS-Lorentz superalgebra
• Gauge Theory of Maxwell-Weyl Group
• Gauge theory of the Maxwell and semi-simple extended (anti) de Sitter algebra
• Generalized cosmological constant from gauging Maxwell-conformal algebra
• Hypersymmetric extensions of Maxwell Chern-Simons gravity in (2+1) dimensions
• $D=4$ supergravity from the Maxwell-Weyl superalgebra
• Three-dimensional Newtonian gravity with cosmological constant and torsion
• Resonant superalgebras and $\mathcal{N}=1$ supergravity theories in three spacetime dimensions
• On Stabilization of Maxwell-BMS Algebra
• Deformation of Asymptotic Symmetry Algebras and Their Physical Realizations
• Gauging the Maxwell extended $\mathcal{G}\mathcal{L}\left(n,\mathbb{R}\right)$ and $\mathcal{SL}\left(n+1,\mathbb{R}\right)$ algebras
• Cosmological application of the Maxwell gravity
• Maxwell-Modified Metric Affine Gravity
• Hietarinta Chern-Simons supergravity and its asymptotic structure
• Three-dimensional non-relativistic Hietarinta supergravity
• Bosonic D=11 supergravity from a generalized Chern-Simons action
• Resonant superalgebras for supergravity
• On the geometric approach to the boundary problem in supergravity
• Modified Friedmann Equations from Maxwell-Weyl Gauge Theory
• Torsion-Induced Modification to Friedmann Equations in $AdS{L}_4$ Gauged Gravity
• $\mathcal{N}=2$ resonant superalgebra for supergravity