We derive new explicit results for the Hilbert series of N=1 supersymmetric QCD with U(N_c) and SU(N_c) color symmetry. We use two methods which have previously been applied to similar computational problems in the analysis of decay of unstable D-bra
nes: expansions using Schur polynomials, and the log-gas approach related to random matrix theory.
We develop a holographic model for thermalization following a quench near a quantum critical point with non-trivial dynamical critical exponent. The anti-de Sitter Vaidya null collapse geometry is generalized to asymptotically Lifshitz spacetime. Non
-local observables such as two-point functions and entanglement entropy in this background then provide information about the length and time scales relevant to thermalization. The propagation of thermalization exhibits similar horizon behavior as has been seen previously in the conformal case and we give a heuristic argument for why it also appears here. Finally, analytic upper bounds are obtained for the thermalization rates of the non-local observables.
We study the high-energy limit of tree-level string production amplitudes from decaying D-branes in bosonic string theory, interpreting the vertex operators as external charges interacting with a Coulomb gas corresponding to the rolling tachyon backg
round, and performing an electrostatic analysis. In particular, we consider two open string - one closed string amplitudes and four open string amplitudes, and calculate explicit formulas for the leading exponential behavior.
We study the partition function of a two-dimensional Coulomb gas on a circle, in the presence of external pointlike charges, in a double scaling limit where both the external charges and the number of gas particles are large. Our original motivation
comes from studying amplitudes for multi-string emission from a decaying D-brane in the high energy limit. We analyze the scaling limit of the partition function and calculate explicit results. We also consider applications to random matrix theory. The partition functions can be related to random scattering, or to weights of lattice paths in certain growth models. In particular, we consider the discrete polynuclear growth model and use our results to compute the cumulative probability density for the height of long level-1 paths. We also obtain an estimate for an almost certain maximum height.
We study vortex solutions in a holographic model of Herzog, Hartnoll, and Horowitz, with a vanishing external magnetic field on the boundary, as is appropriate for vortices in a superfluid. We study relevant length scales related to the vortices and
how the charge density inside the core of the vortex behaves as a function of temperature or chemical potential. We extract the critical superfluid velocity from the vortex solutions, study how it behaves as a function of the temperature, and compare it to earlier studies and to the Landau criterion. We also comment on the possibility of a Berezinskii-Kosterlitz-Thouless vortex confinement-deconfinement transition.
