Abstract:The traditional description of high-energy small-angle scattering in QCD has two components -a soft Pomeron Regge pole for the tensor glueball, and a hard BFKL Pomeron in leading order at weak coupling. On the basis of gauge/string duality, we present a coherent treatment of the Pomeron. In large-N QCD-like theories, we use curved-space string-theory to describe simultaneously both the BFKL regime and the classic Regge regime. The problem reduces to finding the spectrum of a single j-plane Schrödinger operator. For ultraviolet-conformal theories, the spectrum exhibits a set of Regge trajectories at positive t, and a leading j-plane cut for negative t, the cross-over point being model-dependent. For theories with logarithmicallyrunning couplings, one instead finds a discrete spectrum of poles at all t, where the Regge trajectories at positive t continuously become a set of slowly-varying and closely-spaced poles at negative t. Our results agree with expectations for the BFKL Pomeron at negative t, and with the expected glueball spectrum at positive t, but provide a framework in which they are unified. Effects beyond the single Pomeron exchange are briefly discussed.

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We present the analysis of the complete glueball spectrum for the AdS 7 black hole supergravity dual of QCD 4 in strong coupling limit: g 2 N → ∞. The bosonic fields in the supergravity multiplet lead to 6 independent wave equations contributing to glueball states with J P C = 2 ++ , 1 +− , 1 −− , 0 ++ and 0 −+ . We study the spectral splitting and degeneracy patterns for both QCD 4 and QCD 3 . Despite the expected limitations of a leading order strong coupling approximation, the pattern of spins, parities and mass inequalities bare a striking resemblance to the known QCD 4 glueball spectrum as determined by lattice simulations at weak coupling.

We begin the process of unitarizing the Pomeron at large 't Hooft coupling. We do so first in the conformal regime, which applies to good accuracy to a number of real and toy problems in QCD. We rewrite the conformal Pomeron in the J-plane and transverse position space, and then work out the eikonal approximation to multiple Pomeron exchange. This is done in the context of a more general treatment of the complex J-plane and the geometric consequences of conformal invariance. The methods required are direct generalizations of our previous work on single Pomeron exchange and on multiple graviton exchange in AdS space, and should form a starting point for other investigations. We consider unitarity and saturation in the conformal regime, noting elastic and absorptive effects, and exploring where different processes dominate. Our methods extend to confining theories and we briefly consider the Pomeron kernel in this context. Though there is important model dependence that requires detailed consideration, the eikonal approximation indicates that the Froissart bound is generically both satisfied and saturated.

The AdS/CFT correspondence in principle gives a new approach to deep inelastic scattering as formulated by Polchinski and Strassler. Subsequently Brower, Polchinski, Strassler and Tan (BPST) computed the strong coupling kernel for the vacuum (or Pomeron) contribution to total cross sections. By identifying deep inelastic scattering with virtual photon total cross section, this allows a self consistent description at small-x where the dominant contribution is the vacuum exchange process. Here we formulate this contribution and compare it with HERA small-x DIS scattering data. We find that the BPST kernel along with a very simple local approximation to the proton and current "wave functions" gives a remarkably good fit not only at large Q 2 dominated by conformal symmetry but also extends to small Q 2 , supplemented by a hard-wall cut-off of the AdS in the IR. We suggest that this is a useful phenomenological parametrization with implications for other diffractive processes, such as double diffractive Higgs production.

The global phase structure for heterotic string theory is studied. Three different types of representations for thermo-partition functions are provided. We show how modular invariance arises and analyze finite-temperature divergences. A three-phase structure, involving a new nonperturbative hightemperature phase, for the heterotic string is found. The transition into this new phase takes place at B=r;//3, T, where Oh is the conventional "Hagedorn temperature" for the heterotic string.

We explore the eikonal approximation to graviton exchange in AdS 5 space, as relevant to scattering in gauge theories. We restrict ourselves to the regime where conformal invariance of the dual gauge theory holds, and to large 't Hooft coupling where the computation involves pure gravity. We give a heuristic argument, a direct loop computation, and a shock wave derivation. The scalar propagator in AdS 3 plays a key role, indicating that even at strong coupling, two-dimensional conformal invariance controls high-energy four-dimensional gaugetheory scattering. 1 Work with overlapping results appeared [7] as this paper was in preparation. 2 i.e., measured by a local observer in the bulk, 3 In both cases, the cut becomes a discrete and dense set of poles when the coupling runs slowly.

The formalism for discussing energy and charge distribution functions in the microcanonical ensemble is presented and applied to strings. This yields information of direct physical significance in string statistical mechanics. Above the Hagedorn energy density the free string gas exhibits a number of interesting features. For toroidal compactification, the distribution of the total energy among strings of various energies depends upon the number of noncompact spatial dimensions d . For d =O the energy is distributed uniformly among strings at all energy scales, while for d 2 3 a single string captures most of the energy. The imposition of conservation laws does not alter this qualitative picture. We show that the d = 1 and d = 2 cases are qualitatively different from the others.