(2+1)-dimensional supergravity invariant under the AdS-Lorentz superalgebra (original) (raw)
Extended supergravity: Chern–Simons theories in 2+1 dimensions
Journal of Mathematical Physics, 1991
In this paper de Sitter supergravity theories in 2+1 dimensions with positive cosmological constant as Chern–Simons gauge theories of the algebra OSp(M‖2;C) are constructed. Starting from anti-de Sitter supergravity theories based on OSp(M‖2;R)×OSp(M‖2;R) algebras, a particular Inonu–Wigner contraction is used to construct a large class of super Poincaré supergravity theories with nontrivial internal symmetries. Other models based on algebras SL(M‖N) and the exceptional super Lie algebras are also discussed. The classical consistency of our de Sitter supergravity theories is discussed.
Journal of High Energy Physics
In this work we present the ultra-relativistic N-extended AdS Chern-Simons supergravity theories in three spacetime dimensions invariant under N-extended AdS Carroll superalgebras. We first consider the (2, 0) and (1, 1) cases; subsequently, we generalize our analysis to N = (N , 0), with N even, and to N = (p, q), with p, q > 0. The N-extended AdS Carroll superalgebras are obtained through the Carrollian (i.e., ultra-relativistic) contraction applied to an so(2) extension of osp(2|2) ⊗ sp(2), to osp(2|1) ⊗ osp(2, 1), to an so(N) extension of osp(2|N) ⊗ sp(2), and to the direct sum of an so(p) ⊕ so(q) algebra and osp(2|p) ⊗ osp(2, q), respectively. We also analyze the flat limit (→ ∞, being the length parameter) of the aforementioned N-extended Chern-Simons AdS Carroll supergravities, in which we recover the ultra-relativistic N-extended (flat) Chern-Simons supergravity theories invariant under N-extended super-Carroll algebras. The flat limit is applied at the level of the superalgebras, Chern-Simons actions, supersymmetry transformation laws, and field equations.
M ar 2 02 0 N-extended Chern-Simons Carrollian supergravities in 2 + 1 spacetime dimensions
2020
In this work we present the ultra-relativistic N -extended AdS Chern-Simons supergravity theories in three spacetime dimensions invariant under N -extended AdS Carroll superalgebras. We first consider the (2, 0) and (1, 1) cases; subsequently, we generalize our analysis to N = (N , 0), with N even, and to N = (p, q), with p, q > 0. The N -extended AdS Carroll superalgebras are obtained through the Carrollian (i.e., ultra-relativistic) contraction applied to an so(2) extension of osp(2|2) ⊗ sp(2), to osp(2|1) ⊗ osp(2, 1), to an so(N ) extension of osp(2|N ) ⊗ sp(2), and to the direct sum of an so(p) ⊕ so(q) algebra and osp(2|p) ⊗ osp(2, q), respectively. We also analyze the flat limit (l→ ∞, being l the length parameter) of the aforementioned N -extended Chern-Simons AdS Carroll supergravities, in which we recover the ultrarelativistic N -extended (flat) Chern-Simons supergravity theories invariant under N -extended super-Carroll algebras. The flat limit is applied at the level of...
Three-dimensional Poincaré supergravity and N-extended supersymmetric BMS3 algebra
Physics Letters B
A new approach for obtaining the three-dimensional Chern-Simons supergravity for the Poincaré algebra is presented. The N-extended Poincaré supergravity is obtained by expanding the super Lorentz theory. We extend our procedure to their respective asymptotic symmetries and show that the N = (1, 2, 4) super-BMS 3 appear as expansions of one Virasoro superalgebra. Interestingly, the N-extended super-BMS 3 obtained here are not only centrally extended but also endowed with internal symmetry. We also show that the N-extended super Poincaré algebras with both central and automorphism generators are finite subalgebras.
A generalized action for (2 + 1)-dimensional Chern–Simons gravity
Journal of Physics A-mathematical and Theoretical, 2012
We show that the so-called semi-simple extended Poincaré (SSEP) algebra in D dimensions can be obtained from the anti-de Sitter algebra by means of the S-expansion procedure with an appropriate semigroup S. A general prescription is given for computing Casimir operators for S-expanded algebras, and the method is exemplified for the SSEP algebra. The S-expansion method also allows us to
Chern–Simons supergravity inD=3and Maxwell superalgebra
Physics Letters B
We present the construction of the D = 3 Chern-Simons supergravity action from the Maxwell superalgebra sM, which can be obtained from the anti-De Sitter superalgebra by combining the abelian semigroup expansion procedure and the Inönü-Wigner contraction. The Chern-Simons supergravity action from a generalized Maxwell superalgebra is also introduced.
Vector supersymmetry from OSp(3,2|2): Casimir operators
Fortschritte der Physik, 2009
In this paper we briefly review the main results obtained in , where some algebraic properties of the 'vector supersymmetry' (VSUSY) algebra have been studied. VSUSY is a graded extension of the Poincaré algebra in 4 dimensions with two central charges. We derive all independent Casimir operators of VSUSY and we find two distinct spin-related operators in the case of nonvanishing central charges. One is the analogue of superspin for VSUSY and the other is a new spin, called C-spin, whose value is fixed to 1/2. We also show that the VSUSY algebra and its Casimir operators can be derived by an Inönü-Wigner contraction from OSp(3, 2 |2). This paper is based on the talk given in Varna, Bulgaria, during the 4-th EU RTN Workshop 2008.
AdS–MAXWELL SUPERALGEBRA AND SUPERGRAVITY
Modern Physics Letters A, 2012
In this paper we derive the anti-de Sitter counterpart of the super-Maxwell algebra presented recently by Bonanos et al. Then we gauge this algebra and derive the corresponding supergravity theory, which turns out to be described by the standard N = 1 supergravity Lagrangian, up to topological terms.
Vector supersymmetry: Casimir operators and contraction from Ø Sp (3,2 |2)
Journal of High Energy Physics, 2009
We study some algebraic properties of the 'vector supersymmetry' (VSUSY) algebra, a graded extension of the four-dimensional Poincaré algebra with two odd generators, a vector and a scalar, and two central charges. The anticommutator between the two odd generators gives the fourmomentum operator, from which the name vector supersymmetry. We construct the Casimir operators for this algebra and we show how both algebra and Casimirs can be derived by contraction from the simple orthosymplectic algebra OSp(3, 2 |2). In particular, we construct the analogue of superspin for vector supersymmetry and we show that, due to the algebraic structure of the Casimirs, the multiplets are either doublets of spin (s, s + 1) or two spin 1/2 states. Finally, we identify an odd operator, which is an invariant in a subclass of representations where a BPS-like algebraic relation between the mass and the values of the central charges is satisfied.
Contractions yielding new supersymmetric extensions of the poincaré algebra
Reports on Mathematical Physics, 1991
Two new PoincarC superalgebras are analysed. They are obtained by the Wigner-In6nl contraction from two real forms of the superalgebra OSp(2; 4; C) -one describing the N = 2 anti-de-Sitter superalgebra with a non-compact internal symmetry SO(l, 1) and the other corresponding to the de-Sitter superalgebra with internal symmetry SO(2). Both are 19-dimensional self-conjugate extensions of the Konopel'chenko superalgebra. They contain 10 PoincarC generators and one generator of internal symmetry in addition to 8 odd generators half of which, however, do not commute with translations.