We study two-dimensional nonlinear sigma models with target spaces being the complex super Grassmannian manifolds, that is, coset supermanifolds G(m, p|n, q) ∼= U(m|n)/[U(p|q) ⊗ U(m − p|n − q)] for 0 ≤ p ≤ m, 0 ≤ q ≤ n and 1 ≤ p + q. The projective superspace CP is a special case of p = 1, q = 0. For the two-dimensional Euclidean base space, a wide class of exact classical solutions (or harmoni...

The transfer homomorphism from a group G to an abelian subgroup H of finite index in G arises from the natural action of G on the cosets of H. It plays an important role in the study of unsolvable groups and aids in the characterization of groups in which all Sylow p-subgroups are cyclic. In this paper, we will define the transfer homomorphism, and then investigate a few of its properties. Let ...

Green-Schwarz action of Type IIB string on AdS3 × S is constructed via coset superspace approach. The construction relies exclusively on symplectically Majorana-Weyl spinor formalism, thus permitting it easier to prove κ-symmetry for on-shell Type IIB supergravity backgrounds. 1 Work supported in part by the U.S. Department of Energy under Grant No. DE-FG02-90-ER40542, KOSEF Interdisciplinary R...

As been recently pointed out, physically relevant models derived from string theory require the presence of non-vanishing form fluxes besides the usual geometrical constraints. In the case of NS-NS fluxes, the Generalized Complex Geometry encodes these informations in a beautiful geometrical structure. On the other hand, the R-R fluxes call for supergeometry as the underlying mathematical frame...

We address some issues related to the construction of general KaluzaKlein (KK) ansätze for the compactification of a supergravity (sugra) theory on a sphere Sm. We first reproduce various ansätze for compactification to 7d from the ansatz for the full nonlinear KK reduction of 11d sugra on AdS7×S4. As a side result, we obtain a lagrangean formulation of 7d N = 2 gauged sugra, which so far had o...

Following recent advances in the local theory of current-algebraic orbifolds, we study various geometric properties of the general WZW orbifold, the general coset orbifold and a large class of (non-linear) sigma model orbifolds. Phase-space geometry is emphasized for the WZW orbifolds – while for the sigma model orbifolds we construct the corresponding sigma model orbifold action, which include...

In this paper we show how string rewriting methods can be applied to give a new method of computing double cosets. Previous methods for double cosets were enumerative and thus restricted to finite examples. Our rewriting methods do not suffer this restriction and we present some examples of infinite double coset systems which can now easily be solved using our approach. Even when both enumerati...

Coset enumeration is a most important procedure for investigating finitely presented groups. We present a practical parallel procedure for coset enumeration on shared memory processors. The shared memory architecture is particularly interesting because such parallel computation is both faster and cheaper. The lower cost comes when the program requires large amounts of memory, and additional CPU...