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 analyze the finite temperature behavior of the Sakai-Sugimoto model, which is a holographic dual of a theory which spontaneously breaks a U(N_f)_L x U(N_f)_R chiral flavor symmetry at zero temperature. The theory involved is a 4+1 dimensional supersymmetric SU(N_c) gauge theory compactified on a circle of radius R with anti-periodic boundary conditions for fermions, coupled to N_f left-handed quarks and N_f right-handed quarks which are localized at different points on the compact circle (separated by a distance L). In the supergravity limit which we analyze (corresponding in particular to the large N_c limit of the gauge theory), the theory undergoes a deconfinement phase transition at a temperature T_d = 1 / 2 \pi R. For quark separations obeying L > L_c = 0.97 * R the chiral symmetry is restored at this temperature, but for L < L_c = 0.97 * R there is an intermediate phase which is deconfined with broken chiral symmetry, and the chiral symmetry is restored at T = 0.154 / L. All of these phase transitions are of first order.Comment: 30 pages, 7 figures, latex. v2: minor corrections and added reference to parallel wor

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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.

We analyze mesons at finite temperature in a chiral, confining string dual. The temperature dependence of low-spin as well as high-spin meson masses is shown to exhibit a pattern familiar from the lattice. Furthermore, we find the dissociation temperature of mesons as a function of their spin, showing that at a fixed quark mass, mesons with larger spins dissociate at lower temperatures. The Goldstone bosons associated with chiral symmetry breaking are shown to disappear above the chiral symmetry restoration temperature. Finally, we show that holographic considerations imply that large-spin mesons do not experience drag effects when moving through the quark-gluon plasma. They do, however, have a maximum velocity for fixed spin, beyond which they dissociate.

We use the recently proposed supergravity approach to large N gauge theories to calculate ordinary and spatial Wilson loops of gauge theories in various dimensions. In this framework we observe an area law for spatial Wilson loops in four and five dimensional supersymmetric Yang-Mills at finite temperature. This can be interpreted as the area law of ordinary Wilson loops in three and four dimensional non-supersymmetric gauge theories at zero temperature which indicates confinement in these theories. Furthermore, we show that super Yang Mills theories with 16 supersymmetries at finite temperature do not admit phase transitions between the weakly coupled super Yang Mills and supergravity regimes. This result is derived by analyzing the entropy and specific heat of those systems as well as by computing ordinary Wilson loops at finite temperature. The calculation of the entropy was carried out in all different regimes and indicates that there is no first order phase transition in these systems. For the same theories at zero temperature we also compute the dependence of the quark anti-quark potential on the separating distance.

We extend Seiberg's qualitative picture of the behavior of supersymmetric QCD to nonsupersymmetric models by adding soft supersymmetry breaking terms. In this way, we recover the standard vacuum of QCD with N f flavors and N c colors when N f < N c . However, for N f ≥ N c , we find new exotic statesnew vacua with spontaneously broken baryon number for N f = N c , and a vacuum state with unbroken chiral symmetry for N f > N c . These exotic vacua contain massless composite fermions and, in some cases, dynamically generated gauge bosons. In particular Seiberg's electric-magnetic duality seems to persist also in the presence of (small) soft supersymmetry breaking. We argue that certain, specially tailored, lattice simulations may be able to detect the novel phenomena. Most of the exotic behavior does not survive the decoupling limit of large SUSY breaking parameters.

We consider Penrose limits of the Klebanov-Strassler and Maldacena-Núñez holographic duals to N = 1 supersymmetric Yang-Mills. By focusing in on the IR region we obtain exactly solvable string theory models. These represent the nonrelativistic motion and low-lying excitations of heavy hadrons with mass proportional to a large global charge. We argue that these hadrons, both physically and mathematically, take the form of heavy nonrelativistic strings; we term them "annulons." A simple toy model of a string boosted along a compact circle allows us considerable insight into their properties. We also calculate the Wilson loop carrying large global charge and show the effect of confinement is quadratic, not linear, in the string tension.