Résumé: We report on a series of new solutions to five-dimensional minimal supergravity. Our method applies to space-times with two commuting Killing symmetries and consists in combining dimensional reduction on two-spaces of constant curvature with reduction on a two-torus. The first gives rise to various generalized Bertotti-Robinson solutions supported by electric and magnetic fluxes, which presumably describe the near-horizon regions of black holes and black rings (strings). The second provides generating techniques based on U duality of the corresponding three-dimensional sigma model. We identify duality transformations relating the above solutions to asymptotically flat ones and obtain new globally regular dyonic solitons. Some new extremal asymptotically flat multicenter solutions are constructed too. We also show that geodesic solutions of three-dimensional sigma models passing through the same target space point generically split into disjoint classes which cannot be related by the isotropy subgroup of U duality.

Résumé: We present a series of new solutions in five-dimensional Einstein-Maxwell-Chern-Simons theory with an arbitrary Chern-Simons coupling γ and a cosmological constant Λ. For general γ and Λ we give various generalizations of the Bertotti-Robinson solutions supported by electric and magnetic fluxes, some of which presumably describe the near-horizon regions of black strings or black rings. Among them there is a solution which could apply to the horizon of a topological anti–de Sitter black ring in gauged minimal supergravity. Others are horizonless and geodesically complete. We also construct extremal asymptotically flat multistring solutions for Λ=0 and arbitrary γ.

Résumé: In this article we study non-commutative vector sigma model with the most general \phi^4 interaction on Moyal-Weyl spaces. We compute the 2- and 4-point functions to all orders in the large N limit and then apply the approximate Wilson renormalization group recursion formula to study the renormalized coupling constants of the theory. The non-commutative Wilson-Fisher fixed point interpolates between the commutative Wilson-Fisher fixed point of the Ising universality class which is found to lie at zero value of the critical coupling constant a_* of the zero dimensional reduction of the theory, and a novel strongly interacting fixed point which lies at infinite value of a_* corresponding to maximal non-commutativity beyond which the two-sheeted structure of a_* as a function of the dilation parameter disappears.

Résumé: A solution generating technique is developed for D=5 minimal supergravity with two commuting Killing vectors based on the U-duality arising in the reduction of the theory to three dimensions. The target space of the corresponding 3-dimensional sigma-model is the coset G_{2(2)}/(SL(2,R)\times SL(2,R)). Its isometries constitute the set of solution generating symmetries. These include two electric and two magnetic Harrison transformations with the corresponding two pairs of gauge transformations, three SL(2,R) S-duality transformations, and the three gravitational scale, gauge and Ehlers transformations (altogether 14). We construct a representation of the coset in terms of 7\times 7 matrices realizing the automorphisms of split octonions. Generating a new solution amounts to transforming the coset matrices by one-parametric subgroups of G_{2(2)} and subsequently solving the dualization equations. Using this formalism we derive a new charged black ring solution with two independent parameters of rotation.

Résumé: We extend the Abbott-Deser-Tekin approach to the computation of the Killing charge for a solution of topologically massive gravity (TMG) linearized around an arbitrary background. This is then applied to evaluate the mass and angular momentum of black hole solutions of TMG with non-constant curvature asymptotics. The resulting values, together with the appropriate black hole entropy, fit nicely into the first law of black hole thermodynamics.