We find a nonsupersymmetric dilatonic deformation of AdS 5 geometry as an exact nonsingular solution of the type IIB supergravity. The dual gauge theory has a different Yang-Mills coupling in each of the two halves of the boundary spacetime divided by a codimension one defect. We discuss the geometry of our solution in detail, emphasizing the structure of the boundary, and also study the string configurations corresponding to Wilson loops. We also show that the background is stable under small scalar perturbations.

A version of the holographic principle for cosmology is proposed which dictates that the particle entropy within the cosmological apparent horizon should not exceed the gravitational entropy associated with the apparent horizon. It is shown that in Friedmann-Robertson-Walker (FRW) cosmology, the open universe, as well as a restricted class of flat cases, are compatible with the principle, whereas the closed universe is not. It is also found that the inflationary universe after the big bang is incompatible with cosmic holography.

Using the AdS/CFT correspondence, we examine the behavior of correlators of Polyakov loops and other operators in N = 4 supersymmetric Yang-Mills theory at non-zero temperature. The implications for Debye screening in this strongly coupled non-Abelian plasma, and comparisons with available results for thermal QCD, are discussed.

N = 6 superconformal Chern-Simons theory was proposed as gauge theory dual to Type IIA string theory on AdS 4 ⊗ CP 3 . We study integrability of the theory from conformal dimension spectrum of single trace operators at planar limit. At strong 't Hooft coupling, the spectrum is obtained from excitation energy of free superstring on OSp(6|2, 2; R)/SO(3, 1)×SU(3)×U(1) supercoset. We recall that the worldsheet theory is integrable classically by utilizing wellknown results concerning sigma model on symmetric space. With R-symmetry group SU(4), we also solve relevant Yang-Baxter equation for a spin chain system associated with the single trace operators. From the solution, we construct alternating spin chain Hamiltonian involving three-site interactions between 4 and 4. At weak 't Hooft coupling, we study gauge theory perturbatively, and calculate action of dilatation operator to single trace operators up to two loops. To ensure consistency, we computed all relevant Feynman diagrams contributing to the dilatation opeator. We find that resulting spin chain Hamiltonian matches with the Hamiltonian derived from Yang-Baxter equation. We further study new issues arising from the shortest gauge invariant operators TrY I Y † J = (15, 1). We observe that 'wrapping interactions' are present, compute the true spectrum and find that the spectrum agrees with prediction from supersymmetry. We also find that scaling dimension computed naively from alternating spin chain Hamiltonian coincides with the true spectrum. We solve Bethe ansatz equations for small number of excitations, and find indications of correlation between excitations of 4's and 4's and of nonexistence of mesonic (44) bound-state.

We show that the three dimensional Janus geometry can be embedded into the type IIB supergravity and discuss its dual CFT description. We also find exact solutions of time dependent black holes with a nontrivial dilaton field in three and higher dimensions as an application of the Janus construction.

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We find a class of flat supersymmetric brane-antibrane configurations. They follow from ordinary brane-antibrane systems by turning on a specific worldvolume background electric field, which corresponds to dissolved fundamental strings. We have clarified in detail how they arise and identified their constituent charges as well as the corresponding supergravity solutions. Adopting the matrix theory description, we construct the worldvolume gauge theories and prove the absence of any tachyonic degrees. We also study supersymmetric solitons of the worldvolume theories.

We consider the noncommutative Abelian-Higgs theory and investigate general static vortex configurations including recently found exact multi-vortex solutions. In particular, we prove that the self-dual BPS solutions cease to exist once the noncommutativity scale exceeds a critical value. We then study the fluctuation spectra about the static configuration and show that the exact non BPS solutions are unstable below the critical value. We have identified the tachyonic degrees as well as massless moduli degrees. We then discuss the physical meaning of the moduli degrees and construct exact time-dependent vortex configurations where each vortex moves independently. We finally give the moduli description of the vortices and show that the matrix nature of moduli coordinates naturally emerges.