Super-PP-wave Algebra from Super-AdS x S Algebras in Eleven-dimensions

In this work we present the ultra-relativistic $\mathcal{N}$-extended AdS Chern-Simons supergravity theories in three spacetime dimensions invariant under $\mathcal{N}$-extended AdS Carroll superalgebras. We first consider the $(2,0)$ and $(1,1)$ cases; subsequently, we generalize our analysis to $\mathcal{N}=(\mathcal{N},0)$, with $\mathcal{N}$ even, and to $\mathcal{N}=(p,q)$, with $p,q>0$. The $\mathcal{N}$-extended AdS Carroll superalgebras are obtained through the Carrol...

We consider the Penrose limit of AdS$_7$ solutions of massive Type IIA supergravity. The resulting pp-wave geometry is supported by RR and NSNS fields. We quantize the Green--Schwarz superstring on the obtained pp-wave background, in the light-cone gauge.

Locally supersymmetric systems in odd dimensions whose Lagrangians are Chern-Simons forms for supersymmetric extensions of anti-de Sitter gravity are discussed. The construction is illustrated for D=7 and 11. In seven dimensions the theory is an N=2 supergravity whose fields are the vielbein ($e_{\mu}^{a}$), the spin connection ($\omega_{\mu}^{ab}$), two gravitini ($\psi_{\mu}^{i}$) and an $sp(2)$ gauge connection ($a_{\mu j}^{i}$). These fields form a connection for $osp(2|8...

We classify AdS$_3$ solutions preserving $\mathcal{N}=(8,0)$ supersymmetry in ten and eleven dimensions and find the local form of each of them. These include the AdS$_3\times$S$^6$ solution of \cite{Dibitetto:2018ftj} and the embeddings of AdS$_3$ into AdS$_4\times$S$^7$, AdS$_5\times$S$^5$, AdS$_7/\mathbb{Z}_k\times$S$^4$ and its IIA reduction within AdS$_7$. More interestingly we find solutions preserving the superconformal algebras $\mathfrak{f}_4$, $\mathfrak{su}(1,1|4)$...

We describe the linearized supergeometry of eleven dimensional supergravity with four off-shell local supersymmetries. We start with a background Minkowski 11D, N=1 superspace, and an additional ingredient of a global, constant, $G_2$-structure which facilitates the definition of a $4|4+7$ background superspace. A bottom-up construction of linear fluctuations of the geometric constituents (such as supervielbein, spin connection, and the super 3-form of 11D supergravity) is gi...

A new family of supergravity theories in odd dimensions is presented. The Lagrangian densities are Chern-Simons forms for the connection of a supersymmetric extension of the anti-de Sitter algebra. The superalgebras are the supersymmetric extensions of the AdS algebra for each dimension, thus completing the analysis of van Holten and Van Proeyen, which was valid for N=1 and for D=2,3,4,mod 8. The Chern-Simons form of the Lagrangian ensures invariance under the gauge supergrou...

We give an elementary introduction to the structure of supergravity theories. This leads to a table with an overview of supergravity and supersymmetry theories in dimensions 4 to 11. The basic steps in constructing supergravity theories are considered: determination of the underlying algebra, the multiplets, the actions, and solutions. Finally, an overview is given of the geometries that result from the scalars of supergravity theories.

We study the Penrose limit of a supersymmetric IIB background, with non-trivial NS 3-form field strength, obtaining a solution with the smallest number of supercharges (i.e. 16) allowed; we write down explicitly the superalgebra of the theory, build the supersymmetric associated IIB string sigma model and make conjectures on the dual gauge theory.

We consider a supersymmetric extension of the algebra associated with three and four dimensional Anti de Sitter space. A representation of the supersymmetry operators in superspace is given. Supersymmetry invariant models are constructed for the superspace associated with AdS3.

We study supersymmetric AdS_4 x X_7 solutions of 11-dim supergravity where the tri-Sasakian space X_7 has generically U(1)^2\times SU(2)_R isometry. The compact and regular 7-dim spaces X_7=S(t_1,t_2,t_3) is originated from 8-dim hyperkahler quotient of a 12-dim flat hyperkahler space by U(1) and belongs to the class of the Eschenburg space. We calculate the volume of X_7 and that of the supersymmetric five cycle via localization. From this we discuss the 3-dim dual superconf...