Absorption by Threebranes and the AdS/CFT Correspondence

In the first part of this talk I discuss two somewhat different supergravity approaches to calculating correlation functions in strongly coupled Yang-Mills theory. The older approach relates two-point functions to cross-sections for absorption of certain incident quanta by threebranes. In this approach the normalization of operators corresponding to the incident particles is fixed unambiguously by the D3-brane DBI action. By calculating absorption cross-sections of all partial waves of the dilaton we find corresponding two-point functions at strong `t Hooft coupling and show that they are identical to the weak coupling results. The newer approach to correlation functions relates them to boundary conditions in AdS space. Using this method we show that for a certain range of negative mass-squared there are two possible operator dimensions corresponding to a given scalar field in AdS, and indicate how to calculate correlation functions for either of these choices. In the second part of the talk I discuss an example of AdS/CFT duality which arises in the context of type 0 string theory. The CFT on N coincident electric and magnetic D3-branes is argued to be stable for sufficiently weak `t Hooft coupling. It is suggested that its transition to instability at a critical coupling is related to singularity of planar diagrams.Comment: 14 pages, LaTeX; Talk at Strings '99, Potsdam, German

Absorption of dilaton s-wave in type 0B string theory

We find the absorption probability of dilaton field in type 0B string theory. Since the background solutions are of the form $AdS_5 \times S^5$ on both regions, we use the semiclassical formalism adopted in type IIB theory to find the absorption cross section. The background tachyon field solution was used as a reference to relate the solutions of the two regions. We also consider the possible corrections to absorption probability and the $\ln(\ln z)$ form of the correction is expected as in the calculation of the confinement solution.Comment: minor corrections, reference added, version to appear PR

Gauge/string correspondence in curved space

We discuss Gubser-Klebanov-Polyakov proposal for the gauge/string theory correspondence for gauge theories in curved space. Specifically, we consider Klebanov-Tseytlin cascading gauge theory compactified on S^3. We explain regime when this gauge theory is a small deformation of the superconformal N=1 gauge theory on the world volume of regular D3-branes at the tip of the conifold. We study closed string states on the leading Regge trajectory in this background, and attempt to identify the dual gauge theory twist two operators.Comment: 26 pages, v2: refs adde

Schwarzschild Black Holes from Matrix Theory

We consider Matrix theory compactified on T^3 and show that it correctly describes the properties of Schwarzschild black holes in 7+1 dimensions, including the energy-entropy relation, the Hawking temperature and the physical size, up to numerical factors of order unity. The most economical description involves setting the cut-off N in the discretized light-cone quantization to be of order the black hole entropy. A crucial ingredient necessary for our work is the recently proposed equation of state for 3+1 dimensional SYM theory with 16 supercharges. We give detailed arguments for the range of validity of this equation following the methods of Horowitz and Polchinski.Comment: 9 pages, latex; minor typos correcte

Testing Effective String Models of Black Holes with Fixed Scalars

We solve the problem of mixing between the fixed scalar and metric fluctuations. First, we derive the decoupled fixed scalar equation for the four-dimensional black hole with two different charges. We proceed to the five-dimensional black hole with different electric (1-brane) and magnetic (5-brane) charges, and derive two decoupled equations satisfied by appropriate mixtures of the original fixed scalar fields. The resulting greybody factors are proportional to those that follow from coupling to dimension (2,2) operators on the effective string. In general, however, the string action also contains couplings to chiral operators of dimension (1,3) and (3,1), which cause disagreements with the semiclassical absorption cross-sections. Implications of this for the effective string models are discussed.Comment: 13 pages, harvmac; minor typos correcte

N=1 gauge superpotentials from supergravity

We review the supergravity derivation of some non-perturbatively generated effective superpotentials for N=1 gauge theories. Specifically, we derive the Veneziano-Yankielowicz superpotential for pure N=1 Super Yang-Mills theory from the warped deformed conifold solution, and the Affleck-Dine-Seiberg superpotential for N=1 SQCD from a solution describing fractional D3-branes on a C^3 / Z_2 x Z_2 orbifold.Comment: LaTeX, iopart class, 8 pages, 3 figures. Contribution to the proceedings of the workshop of the RTN Network "The quantum structure of space-time and the geometric nature of fundamental interactions", Copenhagen, September 2003; v2: published version with minor clarification

Green's Functions and Non-Singlet Glueballs on Deformed Conifolds

We study the Laplacian on Stenzel spaces (generalized deformed conifolds), which are tangent bundles of spheres endowed with Ricci flat metrics. The (2d-2)-dimensional Stenzel space has SO(d) symmetry and can be embedded in C^d through the equation \sum_{i = 1}^d {z_i^2} = \epsilon^2. We discuss the Green's function with a source at a point on the S^{d-1} zero section of TS^{d-1}. Its calculation is complicated by mixing between different harmonics with the same SO(d) quantum numbers due to the explicit breaking by the \epsilon-deformation of the U(1) symmetry that rotates z_i by a phase. A similar mixing affects the spectrum of normal modes of warped deformed conifolds that appear in gauge/gravity duality. We solve the mixing problem numerically to determine certain bound state spectra in various representations of SO(d) for the d=4 and d=5 examples.Comment: 52 pages, 3 figure

Creation of Fundamental Strings by Crossing D-branes

We study the force balance between orthogonally positioned $p$-brane and $(8-p)$-brane. The force due to graviton and dilaton exchange is repulsive in this case. We identify the attractive force that balances this repulsion as due to one-half of a fundamental string stretched between the branes. As the $p$-brane passes through the $(8-p)$-brane, the connecting string changes direction, which may be interpreted as creation of one fundamental string. We show this directly from the structure of the Chern-Simons terms in the D-brane effective actions. We also discuss the effect of string creation on the 0-brane quantum mechanics in the type I' theory. The creation of a fundamental string is related by U-duality to the creation of a 3-brane discussed by Hanany and Witten. Both processes have a common origin in M-theory: as two M5-branes with one common direction cross, a M2-brane stretched between them is created.Comment: 6 pages, Late

Hadronic Density of States from String Theory

Exactly soluble string theories describing a particular hadronic sector of certain confining gauge theories have been obtained recently as Penrose-Gueven limits of the dual supergravity backgrounds. The effect of taking the Penrose-Gueven limit on the gravity side translates, in the gauge theory side, into an effective truncation to hadrons of large U(1) charge (annulons). We present an exact calculation of the finite temperature partition function for the hadronic states corresponding to a Penrose-Gueven limit of the Maldacena-Nunez embedding of N=1 SYM into string theory. It is established that the theory exhibits a Hagedorn density of states. Motivated by this exact calculation we propose a semiclassical string approximation to the finite temperature partition function for confining gauge theories admitting a supergravity dual, by performing an expansion around classical solutions characterized by temporal windings. This semiclassical approximation reveals a hadronic energy density of states of Hagedorn type, with the coefficient determined by the gauge theory string tension as expected for confining theories. We argue that our proposal captures primarily information about states of pure N=1 SYM, given that this semiclassical approximation does not entail a projection onto states of large U(1) charge.Comment: 15 page