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.

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.

Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodynamics (lattice QCD), where the main computational challenge is to efficiently solve the discretized Dirac equation in the presence of an SU(3) gauge field. Using NVIDIA's CUDA platform we have implemented a Wilson-Dirac sparse matrix-vector product that performs at up to 40, 135 and 212 Gflops for double, single and half precision respectively on NVIDIA's GeForce GTX 280 GPU. We have developed a new mixed precision approach for Krylov solvers using reliable updates which allows for full double precision accuracy while using only single or half precision arithmetic for the bulk of the computation. The resulting BiCGstab and CG solvers run in excess of 100 Gflops and, in terms of iterations until convergence, perform better than the usual defect-correction approach for mixed precision.

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