We find a new Penrose limit of AdS 5 × S 5 that gives the maximally symmetric pp-wave background of Type IIB string theory in a coordinate system that has a manifest space-like isometry. This induces a new pp-wave/gauge-theory duality which on the gauge theory side involves a novel scaling limit of N = 4 SYM theory. The new Penrose limit, when applied to AdS 5 ×S 5 /Z M , yields a pp-wave with a space-like circle. The dual gauge theory description involves a triple scaling limit of an N = 2 quiver gauge theory. We present in detail the map between gauge theory operators and string theory states including winding states, and verify agreement between the energy eigenvalues obtained from string theory and those computed in gauge theory, at least to one-loop order in the planar limit. We furthermore consider other related new Penrose limits and explain how these limits can be understood as part of a more general framework.

We present general formulae for the TsT transformation (T-duality, shift, T-duality) of type II string backgrounds and open string boundary conditions. The TsT transformation provides a systematic procedure to find string theory duals of gauge theories with deformed products of fields in the lagrangian, and the duals can be analyzed by using transformed D-brane probes. As examples illustrating some features of the deformed theories, we consider the known backgrounds dual to non-commutative, dipole and βdeformed N = 4 Super Yang-Mills as well as new backgrounds dual to deformations of the recently proposed N = 6 Chern-Simons-matter theory living on multiple M2-branes on an orbifold.

We present solutions of type IIB supergravity with z = 2 Schrödinger asymptotics that admit an extremal limit, i .e. the black hole horizon has a double zero. These solutions are obtained as TsT transformations of the charged planar black hole in AdS 5 ×S 5 . Unlike the uncharged solution, the Ramond-Ramond two-form is turned on. We study the thermodynamic properties of these new solutions, and we show that the ratio of shear viscosity to entropy density is 1/4π even in the extremal limit. We also consider the TsTtransformed soliton and show that, for a special radius of the compact circle, there is a confinement-deconfinement phase transition at zero temperature between the soliton and black hole phases.

We study extended objects in the gravity dual of the N = 1 β-deformation of N = 4 Super Yang-Mills theory. We identify probe brane configurations corresponding to giant gravitons and Wilson loops. In particular we identify a new class of objects, given by D5-branes wrapped on a two-torus with a world-volume gauge field strength turned on along the torus. These appear when the deformation parameter assumes a rational value and the gauge theory spectrum has additional branches of vacua. We give an interpretation of the new D5-brane dual giant gravitons in terms of rotating vacuum expectation values in these additional branches.

We compare two applications of the gauge/gravity correspondence to a non conformal gauge theory, based respectively on the study of D-branes wrapped on supersymmetric cycles and of fractional D-branes on orbifolds. We study two brane systems whose geometry is dual to N=4, D=2+1 super Yang-Mills theory, the first one describing D4-branes wrapped on a two-sphere inside a Calabi-Yau two-fold and the second one corresponding to a system of fractional D2/D6-branes on the orbifold R^4/Z_2. By probing both geometries we recover the exact perturbative running coupling constant and metric on the moduli space of the gauge theory. We also find a general expression for the running coupling constant of the gauge theory in terms of the "stringy volume" of the two-cycle which is involved in both types of brane systems.Comment: AMS-LaTeX, 35 pages, no figures. Minor typos corrected, version to appear in NP