Search

The Hadamard parametrix is a representation of the short-distance singularity structure of the Feynman Green’s function for a quantum field on a curved spacetime background. Subtracting these divergent terms regularizes the Feynman Green’s function and enables the computation of renormalized expectation values of observables. We study the Hadamard parametrix for a charged, massive, complex scalar field in five spacetime dimensions. Even in Minkowski spacetime, it is not possible to write the Feynman Green’s function for a charged scalar field exactly in closed form. We, therefore, present covariant Taylor series expansions for the biscalars arising in the Hadamard parametrix. On a general spacetime background, we explicitly state the expansion coefficients up to the order required for the computation of the renormalized scalar field current. These coefficients become increasingly lengthy as the order of the expansion increases, so we give the higher-order terms required for the calculation of the renormalized stress-energy tensor in Minkowski spacetime only.

We discuss the properties of matter in a D-dimensional anti-de-Sitter-type space time induced dynamically by the recoil of a very heavy D(irichlet)-particle defect embedded in it. The particular form of the recoil geometry, which from a world-sheet view point follows from logarithmic conformal field theory deformations of the pertinent sigma-models, results in the presence of both infrared and ultraviolet (spatial) cut-offs. These are crucial in ensuring the presence of mass gaps in scalar matter propagating in the D-particle recoil space time. The analogy of this problem with the Liouville-string approach to QCD, suggested earlier by John Ellis and one of the present authors, prompts us to identify the resulting scalar masses with those obtained in the supergravity approach based on the Maldacena's conjecture, but without the imposition of any supersymmetry in our case. Within reasonable numerical uncertainties, we observe that agreement is obtained between the two approaches for a particular value of the ratio of the two cut-offs of the recoil geometry. Notably, our approach does not suffer from the ambiguities of the supergravity approach as regards the validity of the comparison of the glueball masses computed there with those obtained in the continuum limit of lattice gauge theories., Comment: 16 pages LATEX, one LATEX figure incorporated

We discuss the scattering of two light particles in a D-brane background. It is known that, if one light particle strikes the D brane at small impact parameter, quantum recoil effects induce entanglement entropy in both the excited D brane and the scattered particle. In this paper we compute the asymptotic `out' state of a second light particle scattering off the D brane at large impact parameter, showing that it also becomes mixed as a consequence of quantum D-brane recoil effects. We interpret this as a non-factorizing contribution to the superscattering operator S-dollar for the two light particles in a Liouville D-brane background, that appears when quantum D-brane excitations are taken into account., 18 pages LATEX, one figure (incorporated)

Since the formulation of the AdS/CFT correspondence 1, there has been great interest in space-times which are asymptotically anti-de Sitter, and the properties of the Kerr-Newman-anti-de Sitter (KN-AdS) space-time in various dimensions have been extensively studied 2. However, the properties of classical or quantum fields propagating on this background have not been widely studied, and, in particular, the question of whether super-radiance occurs has not been addressed. This is an important issue since a detailed understanding of classical super-radiance is necessary before tackling quantum field theory on rotating black hole geometries 3. We considered a classical scalar field on the KN-AdS background 4, and examined the form of the separated field modes. Given the structure of infinity in asymptotically anti-de Sitter space-times, we paid particular attention to the boundary conditions at infinity. Unlike the situation for asymptotically flat Kerr-Newman black holes 5, super-radiance is not inevitable. It depends partly on our choice of boundary condition at infinity. For reflective boundary conditions at infinity, there is no super-radiance. On the other hand, if we consider transparent boundary conditions at infinity, then the presence of super-radiance depends on our choice of positive frequency. For those KN-AdS black holes possessing a globally time-like Killing vector, then the natural definition of positive frequency implies that there are no super-radiant modes. For other KN-AdS black holes, then this same definition of positive frequency again leads to no super-radiance.