AdS-CFT Research Articles

Spectrum of type IIB supergravity onAdS5×T11:Predictions onN=1SCFT’s

We derive the full Kaluza-Klein spectrum of type IIB supergravity compactified on ${\mathrm{AdS}}_{5}{\ifmmode\times\else\texttimes\fi{}\mathrm{T}}^{11}$ with ${\mathrm{T}}^{11}=SU(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)/U(1).$ From the knowledge of the spectrum and general multiplet shortening conditions, we make a refined test of the AdS-CFT correspondence, by comparison between various shortenings of $SU(2,2|1)$ supermultiplets on ${\mathrm{AdS}}_{5}$ and different families of boundary operators with protected dimensions. Additional towers of long multiplets with rational dimensions, that are not protected by supersymmetry, are also predicted from the supergravity analysis to occur in the SCFT at leading order in N and ${g}_{s}N.$

Curvature dependence of running gauge coupling and confinement in AdS-CFT correspondence

We construct IIB supergravity (viewed as dilatonic gravity) background with non-trivial dilaton and with curved four-dimensional space. Such a background may describe another vacuum of maximally supersymmetric Yang-Mills theory or strong coupling regime of (non)-supersymmetric gauge theory with (power-like) running gauge coupling which depends on curvature. Curvature dependent quark-antiquark potential is calculated where the geometry type of hyperbolic (or de Sitter universe) shows (or not) the tendency of the confinement. Generalization of IIB supergravity background with non-constant axion is presented. Quark-antiquark potential being again curvature-dependent has a possibility to produce the standard area law for large separations.

Holographic normal ordering and multiparticle states in the AdS-CFT correspondence

The general correlator of composite operators of $N=4$ supersymmetric gauge field theory is divergent. We introduce a means for renormalizing these correlators by adding a boundary theory on the AdS space correcting for the divergences. Such renormalizations are not equivalent to the standard normal ordering of current algebras in two dimensions. The correlators contain contact terms that contribute to the OPE; we relate them diagrammatically to correlation functions of compound composite operators dual to multi-particle states.

An Introduction to AdS / CFT correspondence

This is an introduction to the Maldacena conjecture on the equivalence between N = 4 super Yang-Mills in Minkowski space-time and type IIB string theory compactified on AdS5 ⊗ S5.

AdS/CFT Correspondence and Coincident D-6-Branes

A relation between confinement and Maldacena conjecture is briefly discussed. The gauge symmetry enhancement for two coincident D-6-branes is analyzed from the viewpoint of the hypermultiplet low-energy effective action given by the N=2 supersymmetric non-linear sigma-model with the Eguchi-Hanson (ALE) target space.

An Introduction to AdS/CFT Correspondence

This is an introduction to the Maldacena conjecture on the equivalence between N = 4 super Yang-Mills in Minkowski space-time and type IIB string theory compactified on AdS5 ⊗ S5.

Generalized AdS-CFT Correspondence for Matrix Theory in the Large N limit

Generalized AdS-CFT Correspondence for Matrix Theory in the Large N limit

AdS-CFT correspondence for the massive Rarita-Schwinger field

The complete solution to the massive Rarita-Schwinger field equation in anti--de Sitter space is constructed, and used in the AdS-CFT correspondence to calculate the correlators for the boundary conformal field theory. It is found that when no condition is imposed on the field solution, there appear two different boundary conformal field operators, one coupling to a Rarita-Schwinger field and the other to a Dirac field. These two operators are seen to have different scaling dimensions, with that of the spinor-coupled operator exhibiting a nonanalytic mass dependence.

Fundamental versus solitonic description of D3 branes

Type IIB string theory expanded around D3 brane backgrounds describes the dynamics of D3 branes as solitonic objects. On the other hand, there is a fundamental description of them via Polchinski's open strings with Dirichlet boundary conditions. Since these two descriptions describe the dynamics of the same objects, D3 branes, it is natural to believe that they are dual. Therefore at this level, we have a string-string duality as opposed to a string-field theory duality. Once we take the same limits in both descriptions, the Maldacena conjecture in its weaker form follows. We try to make this viewpoint precise and study the implication of it for the stronger form of the Maldacena conjecture.

Consistent nonlinear KK reduction of 11d supergravity on AdS7× S4 and self-duality in odd dimensions

We show that there exists a consistent truncation of 11 dimensional supergravity to the `massless' fields of maximal ( N=4) 7 dimensional gauged supergravity. We find the complete expressions for the nonlinear embedding of the 7 dimensional fields into the 11 dimensional fields, and check them by reproducing the d=7 susy transformation laws from the d=11 laws in various sectors. In particular we determine explicitly the matrix U which connects the Killing spinors to the gravitinos in the KK ansatz, and the dependence of the 4-index field strength on the scalars. This is the first time a complete nonlinear KK reduction of the original d=11 supergravity on a nontrivial compact space has been explicitly given. We need a first order formulation for the 3 index tensor field A ΛΠΣ in d=11 to reproduce the 7 dimensional result. The concept of `self-duality in odd dimensions' is thus shown to originate from first order formalism in higher dimensions. For the AdS-CFT correspondence, our results imply that one can use 7d gauged supergravity (without further massive modes) to compute certain correlators in the d=6 (0,2) CFT at leading order in N. This eliminates an ambiguity in the formulation of the correspondence.

Heterotic–type-I duality, D instantons, and anN=2AdS-CFT correspondence

D-instanton effects are studied for the type-IIB orientifold ${T}^{2}/(\ensuremath{-}{1)}^{{F}_{L}}\ensuremath{\Omega}I$ of Sen using the type-I--heterotic duality. An exact one loop threshold calculation of ${t}_{8}\mathrm{tr}{F}^{4}$ and ${t}_{8}(\mathrm{tr}{F}^{2}{)}^{2}$ terms for the heterotic string on ${T}^{2}$ with Wilson lines breaking SO(32) to $\mathrm{SO}{(8)}^{4}$ is related to D-instanton-induced terms in the world volume of D7 branes in the orientifold. Introducing D3 branes and using the AdS-CFT correspondence in this case, these terms are used to calculate Yang-Mills instanton contributions to four point functions of the large ${N}_{c}$ limit of $N=2$ $\mathrm{USp}{(2N}_{c})$ SYM theory with four fundamental and one antisymmetric tensor hypermultiplets.

Misner string entropy

I show that gravitational entropy can be intrinsically ascribed to spacetimes containing Misner strings (the gravitational analogues of Dirac strings), even in the absence of any other event horizon (or bolt) structures. This result follows from an extension of proposals for evaluating the stress-energy of a gravitational system which are motivated by the AdS-CFT correspondence.

Supergravity, D-brane probes and thermal super Yang-Mills: a comparison

A D3-brane probe in the context of AdS/CFT correspondence at finite temperature is considered. The supergravity predictions for the physical effective couplings of the world-volume gauge theory of the probe brane are compared to those calculated in one-loop perturbation theory in the thermal gauge theory. It is argued that when the Higgs expectation value is much larger than the temperature, the supergravity result must agree with perturbative thermal Yang-Mills. This provides a perturbative test of the Maldacena conjecture. Predictions for the running electric and magnetic effective couplings, beyond perturbation theory are also obtained. Phenomenological applications for universe-branes are discussed. In particular mechanisms are suggested for reducing the induced cosmological constant and naturally obtaining a varying speed of light and a consequent inflation on the universe brane.

Surface terms as counterterms in the AdS-CFT correspondence

We examine the recently proposed technique of adding boundary counterterms to the gravitational action for spacetimes which are locally asymptotic to anti--de Sitter spacetimes. In particular, we explicitly identify higher order counterterms, which allow us to consider spacetimes of dimensions $d<~7.$ As the counterterms eliminate the need of ``background subtraction'' in calculating the action, we apply this technique to study examples where the appropriate background was ambiguous or unknown: topological black holes, Taub-NUT-AdS and Taub-Bolt-AdS. We also identify certain cases where the covariant counterterms fail to render the action finite, and we comment on the dual field theory interpretation of this result. In some examples, the case of a vanishing cosmological constant may be recovered in a limit, which allows us to check results and resolve ambiguities in certain asymptotically flat spacetime computations in the literature.

Regular and irregular boundary conditions in the AdS-CFT correspondence

We expand on the recent proposal of Klebanov and Witten for formulating the AdS-CFT correspondence using irregular boundary conditions. The proposal is shown to be correct to any order in perturbation theory.

Black holes and five-brane thermodynamics

The phase diagram for $\mathrm{D}p$-branes in M theory compactified on ${\mathrm{T}}^{4},{\mathrm{T}}^{4}{/Z}_{2},{\mathrm{T}}^{5},$ and ${\mathrm{T}}^{6}$ is constructed. As for the lower-dimensional tori considered in our previous work [E. Martinec and V. Sahakian, Phys. Rev. D 59, 124005 (1999)], the black brane phase at high entropy connects onto matrix theory at low entropy; we thus recover all known instances of matrix theory as consequences of the Maldacena conjecture. The difficulties that arise for ${\mathrm{T}}^{6}$ are reviewed. We also analyze the D1-D5 system on ${\mathrm{T}}^{5};$ we discuss its relation to matrix models of M5-branes, and use spectral flow as a tool to investigate the dependence of the phase structure on angular momentum.

Can DLCQ test the Maldacena conjecture?

We consider the Maldacena conjecture applied to the near horizon geometry of a D1-brane in the supergravity approximation and consider the possibility of testing the conjecture against the boundary field theory calculation using DLCQ. We propose the two point function of the stress energy tensor as a convenient quantity that may be computed on both sides of the correspondence. On the supergravity side, we may invoke the methods of Gubser, Klebanov, Polyakov, and Witten. On the field theory side, we derive an explicit expression for the two point function in terms of data that may be extracted from a DLCQ calculation at a given harmonic resolution. This gives rise to a well defined numerical algorithm for computing the two point function, which we test in the context of free fermions and the 't Hooft model. For the supersymmetric Yang-Mills theory with 16 supercharges that arises in the Maldacena conjecture, the algorithm is perfectly well defined, although the size of the numerical computation grows too fast to admit any detailed analysis at present, and our results are only preliminary. We are, however, able to present more detailed results on the supersymmetric DLCQ computation of the stress energy tensor correlators for two dimensional Yang Mills theories with (1,1) and (2,2) supersymmetries.

Stress tensors and Casimir energies in the AdS-CFT correspondence

We discuss various approaches to extracting the full stress-energy tensor of the conformal field theory from the corresponding supergravity solutions, within the framework of the Maldacena conjecture. This provides a more refined probe of the AdS-CFT correspondence. We apply these techniques in considering the Casimir energy of the conformal field theory on a torus. It seems that either generically the corresponding supergravity solutions are singular (i.e., involve regions of large string-scale curvatures), or that they are largely insensitive to the boundary conditions of the CFT on the torus.

Multi-instanton calculus and the AdS/CFT correspondence in [formula omitted] superconformal field theory

We present a self-contained study of ADHM multi-instantons in SU( N) gauge theory, especially the novel interplay with supersymmetry and the large- N limit. We give both field- and string-theoretic derivations of the N = 4 supersymmetric multi-instanton action and collective coordinate integration measure. As a central application, we focus on certain n-point functions G n , n = 16, 8 or 4, in N = 4 SU(N) gauge theory at the conformal point (as well as on related higher-partial-wave correlators); these are correlators in which the 16 exact supersymmetric and superconformal fermion zero-modes are saturated. In the large- N limit, for the first time in any four-dimensional theory, we are able to evaluate all leading-order multi-instanton contributions exactly. We find compelling evidence for Maldacena's conjecture: (1) The large = N k-instanton collective coordinate space has the geometry of a single copy of AdS 5 × S 5. (2) The integration measure on this space includes the partition function of ten-dimensional N = 1 SU(k) gauge theory dimensionally reduced to zero dimensions, matching the description of D-instantons in Type IIB string theory. (3) In exact agreement with Type IIB string calculations, at the k-instantonlevel, G n = √N g 8 k n− 7 2 e 2πikτΣ d/k d −2 · F n(x 1, …, x n) , where F n is identical to a convolution of n bulk-to-boundary supergravity propagators.

Multi-instantons and Maldacena's conjecture

We examine certain n-point functions G_n in {\cal N}=4 supersymmetric SU(N) gauge theory at the conformal point. In the large-N limit, we are able to sum all leading-order multi-instanton contributions exactly. We find compelling evidence for Maldacena's conjecture: (1) The large-N k-instanton collective coordinate space has the geometry of AdS_5 x S^5. (2) In exact agreement with type IIB superstring calculations, at the k-instanton level, $G_n = \sqrt{N} g^8 k^{n-7/2} e^{-8\pi^2 k/g^2}\sum_{d|k} d^{-2} \times F_n(x_1,...,x_n)$, where F_n is identical to a convolution of n bulk-to-boundary SUGRA propagators.