N=1,2 4D Superconformal Field Theories and Supergravity in $AdS_5$

The duality between the type IIB superstring theory in an $AdS_5 \times S^5$ background with $N$ units of five-form flux and ${\cal N} =4$ super Yang--Mills theory with a $U(N)$ gauge group has been studied extensively. My version of the construction of the superstring world-sheet action is reviewed here. This paper is dedicated to Michael Duff on the occasion of his 70th birthday.

We overview the main configurations of D-brane probes in the AdS_5 x X^5 background of type IIB string theory (X^5 being a Sasaki-Einstein manifold), and examine their most salient features from the point of view of the dual quiver superconformal field theory.

A method to solve various aspects of the strong coupling expansion of the superconformal field theory duals of AdS_5 x X geometries from first principles is proposed. The main idea is that at strong coupling the configurations that dominate the low energy dynamics of the field theory compactified on a three sphere are given by certain non-trivial semi-classical configurations in the moduli space of vacua. We show that this approach is self-consistent and permits one to expr...

We consider a system of D5/D1 branes in the supergravity background AdS_3xS^3xX, where X is T^4 or K3. By investigating the structure of the missing states in the conformal description, we are able to extend the AdS/CFT correspondence to W algebras. As a test of this new formulation the results are compared to Hilbert schemes and more general supergravity backgrounds as deformations by D3-branes or six-dimensional Calabi-Yau manifolds.

We review extensions of the AdS/CFT correspondence to gauge/ gravity dualities with N=1 supersymmetry. In particular, we describe the gauge/gravity dualities that emerge from placing D3-branes at the apex of the conifold. We consider first the conformal case, with discussions of chiral primary operators and wrapped D-branes. Next, we break the conformal symmetry by adding a stack of partially wrapped D5-branes to the system, changing the gauge group and introducing a logarith...

Spacetime properties of superstrings on AdS_3 x S^3 x S^3 x S^1 are studied. The boundary theory is a two dimensional superconformal field theory with a large N=(4,4) supersymmetry.

We construct global solutions to Type IIB supergravity with 16 residual supersymmetries whose space-time is $AdS_6 \times S^2$ warped over a Riemann surface. Families of solutions are labeled by an arbitrary number $L\geq 3$ of asymptotic regions, in each of which the supergravity fields match those of a $(p,q)$ five-brane, and may therefore be viewed as near-horizon limits of fully localized intersections of five-branes in Type IIB string theory. These solutions provide comp...

We study the duality between string theory on AdS_3 X S^3 X S^3 and two-dimensional conformal theories with large N=4 superconformal algebra A_gamma. We discuss configurations of intersecting branes which give rise to such near-horizon geometries. We compute the Kaluza-Klein spectrum and propose that the boundary superconformal theory can be described by a sigma model on a suitable symmetric product space with a particular choice of anti-symmetric two-form.

Non-supersymmetric d=4 gauge theories which arise from superstring duality on a manifold $AdS_5 \times S_5/Z_p$ are cataloged for a range $2 \leq p \leq 41$. A number have vanishing two-loop gauge \beta-function, a necessary but not sufficient condition to be a conformal field theory.

We study the supergravity dual of four-dimensional ${\mathcal{N}=1}$ superconformal field theories arising from wrapping M5-branes on a K\"ahler two-cycle inside a Calabi-Yau threefold. We derive an effective three-dimensional theory living on the cobordism between the infrared and ultraviolet Riemann surfaces, describing the renormalization group flows between AdS$_7$ and AdS$_{5}$ as well as between different AdS$_{5}$ fixed points. The realization of this system as an effe...