We consider field theories with sixteen supersymmetries, which includes U(N) Yang-Mills theories in various dimensions, and argue that their large N limit is related to certain supergravity solutions. We study this by considering a system of D-branes in string theory and then taking a limit where the brane worldvolume theory decouples from gravity. At the same time we study the corresponding Dbrane supergravity solution and argue that we can trust it in certain regions where the curvature (and the effective string coupling, where appropriate) are small. The supergravity solutions typically have several weakly coupled regions and interpolate between different limits of string-M-theory. IntroductionString theory contains D-branes which are solitonic objects [1]. When we consider the full theory in the presence of these solitons we have modes that propagate in the bulk and modes that propagate on the solitons. The modes on the soliton interact with each other and with the bulk modes. It is possible, however, to define a limit of the full theory in which the bulk modes decouple from the modes living on the D-brane. This is typically a low energy limit, in which we tune the coupling constant so as to keep only the interactions among the modes living on the D-brane. In this limit the D-brane theory becomes super-Yang-Mills (for p ≤ 3). Separating the branes by some distance corresponds in the field theory to giving Higgs expectation values to some fields. Since we want to keep these expectation values finite when we take the limit, we should consider the branes at substringy distances [2].Since D-branes carry some mass and charge they excite the bulk gravity modes and we can find supergravity solutions carrying the same mass and charges. Naively the supergravity solution describes only the long range fields of the D-branes, since we do not expect supergravity to be valid at short distances. General covariance, however, tells us that we can trust the supergravity solution as long as curvatures are locally small compared to the string scale (or the Planck scale). A more careful analysis shows that for a system with a large number of branes, large N, the curvatures are small and we can trust the supergravity solutions even at the substringy distances involved in the decoupling limit described above. The situation is similar to the one studied in [3] for conformal field theories (see also [4,5]). In particular for the 4D N = 4 U(N) super-Yang-Mills theory associated with N D3-branes, it has been argued in [3] that it is "dual" to type IIB string theory on AdS 5 × S 5 in the large N limit.The aim of this paper is to explore analogous connections in the more general case of non-conformal field theories. The supergravity solutions corresponding to p + 1 super-Yang-Mills are black p-brane solutions. They are extended along p + 1 spacetime dimensions. We interpret the radial variable as being related to the energy scale of the process involved. One of the reasons for this interpretation is the fact that a Dp-brane sitting at so...

We study the non-commutative supersymmetric Yang-Mills theory at strong coupling using the AdS/CFT correspondence. The supergravity description and the UV/IR relation confirms the expectation that the non-commutativity affects the ultra-violet but not the infra-red of the Yang-Mills dynamics. We show that the supergravity solution dual to the non-commutative N = 4 SYM in four dimensions has no boundary and defines a minimal scale. We also show that the relation between the B field and the scale of non-commutativity is corrected at large coupling and determine its dependence on the 't Hooft coupling λ. July 1999Classical supersymmetric Yang-Mills theory (SYM) in (p + 1)-dimensional space can be generalized to SYM on non-commutative spaces [1]. Since the generalization involves infinitely many higher order terms, it is very hard to provide a pure field theory proof that such a theory is consistent at the quantum level. String theory provides a way to obtain these theories by considering the decoupling limit of D(p−2)-branes in type II string theories on T 2 with a background NSNS 2-form field B µν polarized along the plane of the torus [2,3]. The fact that non-commutative SYM is obtained from string theory, in a limit which does not involve gravity, suggests (if string theory with constant B field is consistent) that the non-commutative SYM, at least with sixteen supercharges, is a consistent theory at the quantum level.

Recently it was suggested that a graviton in AdS 5 × S 5 with a large momentum along the sphere can blow up into a spherical D-brane in S 5 . In this paper we show that the same graviton can also blow up into a spherical D-brane in AdS 5 with exactly the same quantum numbers (angular momentum and energy). These branes are BPS, preserving 16 of the 32 supersymmetries. We show that there is a BPS classical solution for SYM on S 3 × R with exactly the same quantum numbers. The solution has non-vanishing Higgs expectation values and hence is dual to the large brane in AdS.

It was recently shown that the theory obtained by deforming a general two dimensional conformal theory by the irrelevant operator TT is solvable. In the context of holography, a large class of such theories can be obtained by studying string theory on AdS 3 . We show that a certain single trace TT deformation of the boundary CF T 2 gives rise in the bulk to string theory in a background that interpolates between AdS 3 in the IR and a linear dilaton spacetime in the UV, i.e. to a two dimensional vacuum of Little String Theory. This construction provides holographic duals for a large class of vacua of string theory in asymptotically linear dilaton spacetimes, and sheds light on the UV behavior of TT deformed CF T 2 . It may provide a step towards holography in flat spacetime.

We study the construction of baryons via supergravity along the line suggested recently by Witten and by Gross and Ooguri. We calculate the energy of the baryon as a function of its size. As expected the energy is linear with N . For the non-supersymmetric theories (in three and four dimensions) we find a linear relation which is an indication of confinement. For the N = 4 theory we obtain the result (EL = −const.) which is compatible with conformal invariance. Surprisingly, our calculation suggests that there is a bound state of k quarks if N ≥ k ≥ 5N/8. We study the N = 4 theory also at finite temperature and find the zero temperature behavior for small size of the baryon, and screening behavior for baryon, whose size is large compared to the thermal wavelength.