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

We show how the Killing spinors of some maximally supersymmetric supergravity solutions whose metrics describe symmetric spacetimes (including $AdS,AdS\times S$ and H$pp$-waves) can be easily constructed using purely geometrical and group-theoretical methods. The calculation of the supersymmetry algebras is extremely simple in this formalism.

We construct a new extension of the Poincar\'e superalgebra in eleven dimensions which contains super one-, two- and five-form charges. The latter two are associated with the supermembrane and the superfivebrane of M-theory. Using the Maurer-Cartan equations of this algebra, we construct closed super seven-forms in a number of ways. The pull-back of the corresponding super six-forms are candidate superfivebrane Wess-Zumino terms, which are manifestly supersymmetric, and conta...

In this paper we study supersymmetric field theories on an AdS_p x S^q space-time that preserves their full supersymmetry. This is an interesting example of supersymmetry on a non-compact curved space. The supersymmetry algebra on such a space is a (p-1)-dimensional superconformal algebra, and we classify all possible algebras that can arise for p >= 3. In some AdS_3 cases more than one superconformal algebra can arise from the same field theory. We discuss in detail the spec...

A new N=4 superconformal algebra (SCA) is presented. Its internal affine Lie algebra is based on the seven-dimensional Lie algebra su(2)\oplus g, where g should be identified with a four-dimensional non-reductive Lie algebra. Thus, it is the first known example of what we choose to call a non-reductive SCA. It contains a total of 16 generators and is obtained by a non-trivial In\"on\"u-Wigner contraction of the well-known large N=4 SCA. The recently discovered asymmetric N=4 ...

In the $N=1$ superspace, AdS$_4$ supersymmetry is realized as the non-linear super coordinate transformations. The fermionic coordinates form a faithful non-linear representation of supersymmetry on their own. By introducing an auxiliary scalar coordinate, this representation is reformulated as a 5-dimensional linear representation, i.e., the superspinor representation. New linear representations are constructed by tensor products of multiple superspinors. Especially, the sup...

Using canonical forms on S^7, viewed as an SU(2) bundle over S^4, we introduce consistent ansatze for the 4-form field strength of eleven-dimensional supergravity and rederive the known squashed, stretched, and the Englert solutions. Further, by rewriting the metric of S^7 as a U(1) bundle over CP^3, we present yet more general ansatze. As a result, we find a new compactifying solution of the type AdS_5\times CP^3, where CP^3 is stretched along its S^2 fiber. We also find a n...

We consider supersymmetric PP-wave limits for different N=1 orbifold geometries of the five sphere S^5 and the five dimensional Einstein manifold T^{1,1}. As there are several interesting ways to take the Penrose limits, the PP-wave geometry can be either maximal supersymmetric N=4 or half-maximal supersymmetric N=2. We discuss in detail the cases AdS_5 x S^5/Z_3, AdS_5 x S^5/(Z_m x Z_n) and AdS_5 x T^{1,1}/(\Z_m \times \Z_n) and we identify the gauge invariant operators whic...

New techniques based on Exceptional Field Theory have recently allowed for the calculation of the Kaluza-Klein spectra of certain AdS$_4$ solutions of $D=11$ and massive IIA supergravity. These are the solutions that consistently uplift on $S^7$ and $S^6$ from vacua of maximal four-dimensional supergravity with SO(8) and ISO(7) gaugings. In this paper, we provide the complete Kaluza-Klein spectrum of five such AdS$_4$ solutions, all of them ${\cal N}=1$. These solutions prese...

We derive anticommutators of supercharges with a brane charge for a D-particle in AdS(2) x S(2) and pp-wave backgrounds. A coset GL(2|2)/(GL(1))^4 and its Penrose limit are used with the supermatrix-valued coordinates for the AdS and the pp-wave spaces respectively. The brane charges have position dependence, and can be absorbed into bosonic generators by shift of momenta which results in closure of the superalgebras.

We consider simple superalgebras which are a supersymmetric extension of $\fspin(s,t)$ in the cases where the number of odd generators does not exceed 64. All of them contain a super Poincar\'e algebra as a contraction and another as a subalgebra. Because of the contraction property, some of these algebras can be interpreted as de Sitter or anti de Sitter superalgebras. However, the number of odd generators present in the contraction is not always minimal due to the different...