Minimal AdS-Lorentz supergravity in three-dimensions

Abstract

The $\mathcal{N}=1$ AdS-Lorentz superalgebra is studied and its relationship to semigroup expansion developed. Using this mathematical tool, the invariant tensors and Casimir operators are found. In terms of these invariants, a three-dimensionnal Chern--Simons supergravity action with AdS-Lorentz symmetry is constructed. The Killing spinors for a BTZ black-hole like solution of the theory are discussed.

18 pages, matches published version

References in corpus (18)

• Newtonian Gravity and the Bargmann Algebra
• Expanding Lie (super)algebras through abelian semigroups
• Asymptotic symmetries and dynamics of three-dimensional flat supergravity
• Expansions of algebras and superalgebras and some applications
• Topological gravity and transgression holography
• 2 + 1 dimensional gravity from Maxwell and semi-simple extension of the Poincare gauge symmetric models
• A generalized action for $\left(2+1\right)$-dimensional Chern--Simons gravity
• Generating infinite-dimensional algebras from loop algebras by expanding Maurer Cartan forms
• Asymptotic symmetries of three-dimensional Chern-Simons gravity for the Maxwell algebra
• The Extended Cartan Homotopy Formula and a Subspace Separation Method for Chern--Simons Theory
• Eleven-Dimensional Gauge Theory for the M Algebra as an Abelian Semigroup Expansion of osp(32|1)
• Generalizing the ${\mathfrak{bms}}_3$ and 2D-conformal algebras by expanding the Virasoro algebra
• Chern-Simons Supergravity in D=3 and Maxwell superalgebra
• Inönü-Wigner Contraction and $D=2+1$ Supergravity
• Supersymmetric 3D model for gravity with $SU(2)$ gauge symmetry, mass generation and effective cosmological constant
• Generalized Galilean Algebras and Newtonian Gravity
• Semi-simple $o(N)$-extended super-Poincaré algebra
• Transgression forms as source for topological gravity and Chern-Simons-Higgs theories

Cited by in corpus (25)

• Pure Lovelock gravity and Chern-Simons theory
• On the Maxwell supergravity and flat limit in 2+1 dimensions
• Generalized Chern-Simons higher-spin gravity theories in three dimensions
• Chern-Simons Supergravity in D=3 and Maxwell superalgebra
• Non-Relativistic Gravity Theory based on an Enlargement of the Extended Bargmann Algebra
• New family of Maxwell like algebras
• Spontaneously Broken 3d Hietarinta/Maxwell Chern-Simons Theory and Minimal Massive Gravity
• $\mathcal{N}$-extended Maxwell supergravities as Chern-Simons theories in three spacetime dimensions
• Non-relativistic three-dimensional supergravity theories and semigroup expansion method
• 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 Gauss-Bonnet like Gravity
• On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions
• Three-dimensional Maxwellian Extended Newtonian gravity and flat limit
• Semi-simple enlargement of the ${\mathfrak{bms}}_3$ algebra from a $\mathfrak{so}(2,2)\oplus \mathfrak{so}(2,1)$ Chern-Simons theory
• Generalized cosmological term in D=4 supergravity from a new AdS-Lorentz superalgebra
• An Analytic Method for $S$-Expansion involving Resonance and Reduction
• Generalized AdS-Lorentz deformed supergravity on a manifold with boundary
• Three-dimensional Newtonian gravity with cosmological constant and torsion
• Resonant superalgebras and $\mathcal{N}=1$ supergravity theories in three spacetime dimensions
• On a Java library to perform S-expansions of Lie algebras
• A Java library to perform S-expansions of Lie algebras
• On the geometric approach to the boundary problem in supergravity
• Three-dimensional Maxwellian Carroll gravity theory and the cosmological constant
• $\mathcal{N}=2$ resonant superalgebra for supergravity