We characterize topological spaces which are coset of (separable) metrizable groups and complete (Polish) groups. Moreover, it is shown that for a $G$-space $X$ with $d$-open action there group $H$ weight cardin

In heterotic string theory compactified on T , the T-duality orbits of dyons of charge (Q,P ) are characterized by O(6, 22; R ) invariants Q, P 2 and Q · P together with a set of invariants of the discrete T-duality group O(6, 22; ZZ). We study the action of S-duality group on the discrete T-duality invariants and study its consequence for the dyon degeneracy formula. In particular we find that...

There are q+q right PGL2(Fq)−cosets in the group PGL2(Fq2). In this paper, we present a method of generating all the coset representatives, which runs in time Õ(q), thus achieves the optimal time complexity up to a constant factor. Our algorithm has applications in solving discrete logarithms and finding primitive elements in finite fields of small characteristic.

We develop a systematic method to construct the boundary states in the coset conformal field theory G/H . Based on the relation of the G/H theory with the tensor product theory G×H , we give a map from the boundary states of G×H to those of G/H . Our map provides a large class of boundary states in coset theories, which include those not factorizable into the G and the H sectors. The action of ...

Among the familiar basic facts concerning unrestricted permutational wreath products (sketched in the first few paragraphs of the last section of Cossey, Kegel, and Kov~cs [2]), the Embedding Theorem has the central role. It asserts the existence of an embedding; the proof is a construction which involves arbitrarily chosen coset representatives, with the effect that the embedding constructed m...

A description is given of how to construct (0, 2) supersymmetric conformal field theories as coset models. These models may be used as non–trivial backgrounds for Heterotic String Theory. They are realised as a combination of an anomalously gauged Wess–Zumino–Witten model, right–moving supersymmetric fermions, and left–moving current algebra fermions. Requiring the sum of the gauge anomalies fr...

M/string theory on noncompact, negatively curved, cosets which generalize AdSD+1 = SO(D, 2)/SO(D, 1) is considered. Holographic descriptions in terms of a conformal field theory on the boundary of the spacetime are proposed. Examples include SU(2, 1)/U(2), which is a Euclidean signature (4, 0) space with no supersymmetry, and SO(2, 2)/SO(2) and SO(3, 2)/SO(3), which are Lorentzian signature (4,...