Dissipative force on an external quark in heavy quark cloud

Within the finite temperature N = 4 strongly coupled super Yang- Mills, we compute the dissipative force on an external quark in the presence of evenly distributed heavy quark cloud. This is computed holographically by constructing the corresponding gravity dual. We study the behaviour of this force as a function of the cloud density. Along the way we also analyze the stability of the gravity dual for vector and tensor perturbations.Comment: 14 pages, 2 figures, significant improvements, to be appeared in Physics Letters

On a Nielsen-Thurston classification theory for cluster modular groups

We classify elements of a cluster modular group into three types. We characterize them in terms of fixed point property of the action on the tropical compactifications associated with the corresponding cluster ensemble. The characterization gives an analogue of the Nielsen-Thurston classification theory on the mapping class group of a surface.Comment: 33 pages, 9 figures. To appear in Annales de l'Institut Fourie

Comments on Takahashi-Tanimoto's scalar solution

We study the identity-based solution of Witten's cubic bosonic open string field theory constructed by Takahashi and Tanimoto, which is claimed to describe the tachyon vacuum. We argue that the observables of the solution coincide with those of the tachyon vacuum using the method proposed by Kishimoto and Takahashi. We also discuss how to treat the kinetic term of the string field theory expanded around it.Comment: 25 pages, 4 figures, v3: several clarifications added, corrected statements about operator U, v4: comments on operator U_k are adde

Higher Dimensional Bondi Energy with a Globally Specified Background Structure

A higher (even spacetime) dimensional generalization of the Bondi energy has recently been proposed by gr-qc/0304054 within the framework of conformal infinity and Hamiltonian formalizm. The gauge condition employed in gr-qc/0304054 to derive the Bondi energy expression is, however, peculiar in the sense that cross-sections of null infinity specified by that gauge are anisotropic and in fact non-compact. For this reason, that gauge is difficult to use for explicit computations of the Bondi energy in general, asymptotically flat radiative spacetimes. Also it is not clear, under that gauge condition, whether apparent difference between the expressions of higher dimensional Bondi energy and the 4-dimensional one is due to the choice of gauges or qualitatively different nature of higher dimensional gravity from 4-dimensional gravity. In this paper, we consider instead, Gaussian null conformal gauge as one of more natural gauge conditions that admit a global specification of background structure with compact, spherical cross-sections of null infinity. Accordingly, we modify the previous definition of higher dimensional news tensor so that it becomes well-defined in the Gaussian null conformal gauge and derive, for vacuum solutions, the expression for the Bondi energy-momentum in the new gauge choice, which takes a universal form in arbitrary (even spacetime) dimensions greater than or equal to four.Comment: 23 pages, no figures, references are added, minor corrections, numerous minor revisions, to appear in Class. Quantum Gra

A master equation for gravitational perturbations of maximally symmetric black holes in higher dimensions

We show that in four or more spacetime dimensions, the Einstein equations for gravitational perturbations of maximally symmetric vacuum black holes can be reduced to a single 2nd-order wave equation in a two-dimensional static spacetime for a gauge-invariant master variable, irrespective of the mode of perturbations. Our formulation applies to the case of vanishing as well as non-vanishing cosmological constant Lambda. The sign of the sectional curvature K of each spatial section of equipotential surfaces is also kept general. In the four-dimensional Schwarzschild background, this master equation for a scalar perturbation is identical to the Zerilli equation for the polar mode and the master equation for a vector perturbation is identical to the Regge-Wheeler equation for the axial mode. Furthermore, in the four-dimensional Schwarzschild-anti-de Sitter background with K=0,1, our equation coincides with those derived by Cardoso and Lemos recently. As a simple application, we prove the perturbative stability and uniqueness of four-dimensional non-extremal spherically symmetric black holes for any Lambda. We also point out that there exists no simple relation between scalar-type and vector-type perturbations in higher dimensions, unlike in four dimensions. Although we only treat maximally symmetric black holes in the present paper, the final master equations are valid even when the hirozon geometry is described by a generic Einstein manifold.Comment: 22 pages in the PTP TeX style, no figure. The published versio