Using sigma-model approach, we study a class of coset spaces with torsion which compactify the D = 26 closed bose-string theory. Requiring also that massless chiral fermions arise from the geometry/topology of coset space, we are left with the unique possibility: it implies D = 14 subcritical dimensions and the isometry group G 2 × G 2 .

We prove a result on certain finite index subgroups of rank one lattices which is motivated by cusp closing constructions. Let X always denote a rank one symmetric space of non-compact type, i.e., X is the hyperbolic space KH, n ≥ 2, where K is either R,C,H or O and n = 2 in the latter case. By Σ we always denote a lattice in the isometry group Iso(X), that is, a discrete subgroup of the isomet...

Orthogonal Matching Pursuit (OMP) is a simple, yet empirically competitive algorithm for sparse recovery. Recent developments have shown that OMP guarantees exact recovery of K-sparse signals in K iterations if the observation matrix Φ satisfies the Restricted Isometry Property (RIP) with Restricted Isometry Constant (RIC) δK+1 < 1

We prove: For all n and all n-cylic isometriesφ : ΛQ → ΛQ of the rational K3 lattice there exists an algebraic realization of φ, i.e. marked algebraic K3 surfaces (S,ηS) and (M,ηM), whereM is a moduli space of sheaves on S, and a Hodge isometry ψ : H2(S,Q)→ H2(M,Q) such that φ = ηM ◦ψ ◦ η−1 S . 1 Facts about cyclic isometries We need the existence of a triple ((S,ηS), (M,ηM),ψ) to have a point ...

Let X be a proper hyperbolic geodesic metric space of bounded growth and let G be a closed subgroup of the isometry group Iso(X) of X. We show that if G is not amenable then the second continuous bounded cohomol-ogy group H 2 cb (G, L 2 (G)) does not vanish. As an application, we derive some structure results for closed subgroups of Iso(X).

We study a Hanany-Witten set-up relevant to N = 2 superconformal field theories. We find the exact near-horizon solution for this 11-dimensional system which involves intersecting M5-branes. The metric describes a warped product of AdS5 with a manifold with SU(2) ×U(1) isometry. USITP-00-08 DTP/00/45 hep-th/0006060 email: [email protected] email: [email protected]