April 27, 1998
We show that five-dimensional anti de-Sitter space remains a solution to low-energy type IIB supergravity when the leading higher-derivative corrections to the classical supergravity (which are non-perturbative in the string coupling) are included. Furthermore, at this order in the low energy expansion of the IIB theory the graviton two-point and three-point functions in $AdS_5 \times S^5$ are shown not to be renormalized and a precise expression is obtained for the four-graviton and related S-matrix elements. By invoking Maldacena's conjectured connection between IIB superstring theory and supersymmetric Yang-Mills theory corresponding statements are obtained concerning correlation functions of the energy-momentum tensor and related operators in the large-N Yang-Mills theory. This leads to interesting non-perturbative statements and insights into the r\^ole of instantons in the gauge theory.
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May 9, 2002
N=4 supersymmetric Yang-Mills theory with gauge group SU(n) (n>=3) is believed to have two exactly marginal deformations which break the supersymmetry to N=1. We discuss the construction of the string theory dual to these deformations, in the supergravity approximation, in a perturbation series around the AdS_5 * S^5 solution. We construct explicitly the deformed solution at second order in the deformation. We show that deformations which are marginal but not exactly marginal...
July 3, 1998
The one-instanton contributions to various correlation functions of supercurrents in four-dimensional N=4 supersymmetric SU(2) Yang-Mills theory are evaluated to the lowest order in perturbation theory.Expressions of the same form are obtained from the leading effects of a single D-instanton extracted from the IIB superstring effective action around the AdS5*S5 background. This is in line with the suggested AdS/Yang-Mills correspondence. The relation between Yang--Mills insta...
November 6, 1998
We report on the computation of the one-instanton contribution to the 16-point Green function of fermionic composite operators in N=4 Super YM theory. The remarkable agreement, initially found in the case of an SU(2) gauge group, with the one D-instanton contribution to the corresponding type IIB superstring amplitude on $AdS_5\times S^5$ is reviewed here. The recent extension by other authors of this result to any SU(N) gauge group and to multi-instantons in the large N limi...
December 31, 2018
We study non-planar correlators in ${\cal N}=4$ super-Yang-Mills in Mellin space. We focus in the stress tensor four-point correlator to order $1/N^4$ and in a strong coupling expansion. This can be regarded as the genus-one four-point graviton amplitude of type IIB string theory on $AdS_5 \times S^5$ in a low energy expansion. Both the loop supergravity result as well as the tower of stringy corrections have a remarkable simple structure in Mellin space, making manifest impo...
August 26, 1999
This dissertation reviews various aspects of the N=4 supersymmetric Yang--Mills theory in particular in relation with the AdS/CFT correspondence. The first two chapters are introductory. The first one contains a description of the general properties of rigid supersymmetric theories in four dimensions both at the classical and at the quantum level. The second chapter is a review of the main properties of the N=4 SYM theory under consideration. Original results are reported in ...
November 10, 2000
A survey of ideas, techniques and results from d=5 supergravity for the conformal and mass-perturbed phases of d=4 ${\cal N}$=4 Super-Yang-Mills theory
July 3, 2003
In a certain kinematic limit, where the effects of spacetime curvature (and other background fields) greatly simplify, the light-cone gauge world-sheet action for a type IIB superstring on AdS_5 x S^5 reduces to that of a free field theory. It has been conjectured by Berenstein, Maldacena, and Nastase that the energy spectrum of this string theory matches the dimensions of operators in the appropriately defined large R-charge large-N_c sector of N=4 supersymmetric Yang--Mills...
February 28, 1999
This is an introduction to the Maldacena conjecture on the equivalence between ${\cal{N}}=4$ super Yang-Mills in Minkowski space-time and type IIB string theory compactified on $AdS_5 \otimes S_5 $.
April 20, 2020
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.
August 25, 1998
We examine a certain 16-fermion correlator in {\cal N}=4 supersymmetric SU(N) gauge theory in 4 dimensions. Generalizing recent SU(2) results of Bianchi, Green, Kovacs and Rossi, we calculate the exact N-dependence of the effective 16-fermion vertex at the 1-instanton level, and find precise agreement in the large-N limit with the prediction of the type IIB superstring on AdS_5 x S^5. This suggests that the string theory prediction for the 1-instanton amplitude considered her...