A Note on the Holographic Beta and C Functions

The holographic RG flow in AdS/CFT correspondence naturally defines a holographic scheme in which the central charge c and the beta function are related by a universal formula. We perform some checks of that formula and we compare it with quantum field theory expectations. We discuss alternative definitions of the c-function. In particular, we compare, for a particular supersymmetric flow, the holographic c-function with the central charge computed directly from the two-point function of the stress-energy tensor.Comment: Version accepted for publication in Phys. Lett. B, expanded introduction. 11 pages, 2 embedded eps figure

Nuclear Flow Excitation Function

We consider the dependence of collective flow on the nuclear surface thickness in a Boltzmann--Uehling--Uhlenbeck transport model of heavy ion collisions. Well defined surfaces are introduced by giving test particles a Gaussian density profile of constant width. Zeros of the flow excitation function are as much influenced by the surface thickness as the nuclear equation of state, and the dependence of this effect is understood in terms of a simple potential scattering model. Realistic calculations must also take into account medium effects for the nucleon--nucleon cross section, and impact parameter averaging. We find that balance energy scales with the mass number as $A^{-y}$, where $y$ has a numerical value between 0.35 and 0.5, depending on the assumptions about the in-medium nucleon-nucleon cross section.Comment: 11 pages (LaTeX), 7 figures (not included), MSUCL-884, WSU-NP-93-

Relativistic Radiative Flow in a Luminous Disk

Radiatively driven transfer flow perpendicular to a luminous disk was examined under a fully special relativistic treatment, taking into account radiation transfer. The flow was assumed to be vertical, and the gravity, the gas pressure, and the viscous heating were ignored. In order to construct the boundary condition at the flow top, the magic speed above the flat source was re-examined, and it was found that the magic speed above a moving source can exceed that above a static source ($\sim 0.45~c$). Then, the radiatively driven flow in a luminous disk was numerically solved, from the flow base (disk ``inside''), where the flow speed is zero, to the flow top (disk ``surface''), where the optical depth is zero. For a given optical depth and appropriate initial conditions at the flow base, where the flow starts, a loaded mass in the flow was obtained as an eigenvalue of the boundary condition at the flow top. Furthermore, a loaded mass and the flow final speed at the flow top were obtained as a function of the radiation pressure at the flow base; the flow final speed increases as the loaded mass decreases. Moreover, the flow velocity and radiation fields along the flow were obtained as a function of the optical depth. Within the present treatment, the flow three velocity $v$ is restricted to be within the range of $v < c/\sqrt{3}$, which is the relativistic sound speed, due to the relativistic effect.Comment: 8 pages, 5 figure

Three-Prong Distribution of Massive Narrow QCD Jets

We study the planar-flow distributions of narrow, highly boosted, massive QCD jets. Using the factorization properties of QCD in the collinear limit, we compute the planar-flow jet function from the one-to-three splitting function at tree-level. We derive the leading-log behavior of the jet function analytically. We also compare our semi-analytic jet function with parton-shower predictions using various generators.Comment: 59 pages, 9 figure

Nonlinear Hydrodynamics from Flow of Retarded Green's Function

We study the radial flow of retarded Green's function of energy-momentum tensor and $R$-current of dual gauge theory in presence of generic higher derivative terms in bulk Lagrangian. These are first order non-linear Riccati equations. We solve these flow equations analytically and obtain second order transport coefficients of boundary plasma. This way of computing transport coefficients has an advantage over usual Kubo approach. The non-linear equation turns out to be a linear first order equation when we study the Green's function perturbatively in momentum. We consider several examples including $Weyl^4$ term and generic four derivative terms in bulk. We also study the flow equations for $R$-charged black holes and obtain exact expressions for second order transport coefficients for dual plasma in presence of arbitrary chemical potentials. Finally we obtain higher derivative corrections to second order transport coefficients of boundary theory dual to five dimensional gauge supergravity.Comment: Version 2, reference added, typos correcte