Classical and quantum geometrodynamics of 2d vacuum dilatonic black holes

We perform a canonical analysis of the system of 2d vacuum dilatonic black holes. Our basic variables are closely tied to the spacetime geometry and we do not make the field redefinitions which have been made by other authors. We present a careful discssion of asymptotics in this canonical formalism. Canonical transformations are made to variables which (on shell) have a clear spacetime significance. We are able to deduce the location of the horizon on the spatial slice (on shell) from the vanishing of a combination of canonical data. The constraints dramatically simplify in terms of the new canonical variables and quantization is easy. The physical interpretation of the variable conjugate to the ADM mass is clarified. This work closely parallels that done by Kucha{\v r} for the vacuum Schwarzschild black holes and is a starting point for a similar analysis, now in progress, for the case of a massless scalar field conformally coupled to a 2d dilatonic black hole.Comment: 21 pages, latex fil

Real decoupling ghost quantization of the CGHS model for two dimensional black holes

A complete RST quantization of a CGHS model plus Strominger term is carried out. In so doing a conformal invariant theory with $\kappa=\frac{N}{12}$ is found, that is, without ghosts contribution. The physical consequences of the model are analysed and positive definite Hawking radiation is found.Comment: 14 pages, latex, no figures, marginal errors correcte

Hamiltonian Approach to 2D Dilaton-Gravities and Invariant Adm Mass

The formula existing in the literature for the ADM mass of 2D dilaton gravity is incomplete. For example, in the case of an infalling matter shockwave this formula fails to give a time-independent mass, unless a very special coordinate system is chosen. We carefully carry out the canonical formulation of 2D dilaton gravity theories (classical, CGHS and RST). As in 4D general relativity one must add a boundary term to the bulk Hamiltonian to obtain a well-defined variational problem. This boundary term coincides with the numerical value of the Hamiltonian and gives the correct mass which obviously is time-independent.Comment: revised, 12 pages, PUPT-1379; we added a reference and corrected some minor typo

Classical A_n--W-Geometry

This is a detailed development for the $A_n$ case, of our previous article entitled "W-Geometries" to be published in Phys. Lett. It is shown that the $A_n$--W-geometry corresponds to chiral surfaces in $CP^n$. This is comes out by discussing 1) the extrinsic geometries of chiral surfaces (Frenet-Serret and Gauss-Codazzi equations) 2) the KP coordinates (W-parametrizations) of the target-manifold, and their fermionic (tau-function) description, 3) the intrinsic geometries of the associated chiral surfaces in the Grassmannians, and the associated higher instanton- numbers of W-surfaces. For regular points, the Frenet-Serret equations for $CP^n$--W-surfaces are shown to give the geometrical meaning of the $A_n$-Toda Lax pair, and of the conformally-reduced WZNW models, and Drinfeld-Sokolov equations. KP coordinates are used to show that W-transformations may be extended as particular diffeomorphisms of the target-space. This leads to higher-dimensional generalizations of the WZNW and DS equations. These are related with the Zakharov- Shabat equations. For singular points, global Pl\"ucker formulae are derived by combining the $A_n$-Toda equations with the Gauss-Bonnet theorem written for each of the associated surfaces.Comment: (60 pages

Two Dimensional Quantum Dilaton Gravity and the Positivity of Energy

Using an argument due to Regge and Teitelboim, an expression for the ADM mass of 2d quantum dilaton gravity is obtained. By evaluating this expression we establish that the quantum theories which can be written as a Liouville-like theory, have a lower bound to energy, provided there is no critical boundary. This fact is then reconciled with the observation made earlier that the Hawking radiation does not appear to stop. The physical picture that emerges is that of a black hole in a bath of quantum radiation. We also evaluate the ADM mass for the models with RST boundary conditions and find that negative values are allowed. The Bondi mass of these models goes to zero for large retarded times, but becomes negative at intermediate times in a manner that is consistent with the thunderpop of RST.Comment: 16 pages, phyzzx, COLO-HEP-309. (Confusing points in previous version clarified, discussion of ADM and Bondi masses in RST case added.

Canonical Quantization of Interacting WZW Theories

Using canonical quantization we find the Virasoro centre for a class of conformally-invariant interacting Wess-Zumino-Witten theories. The theories have a group structure similar to that of Toda theories (both abelian and non-abelian) but the usual Toda constraints on the coupling constants are relaxed and the theories are not necessarily integrable. The general formula for the Virasoro centre is compared to that derived by BRST methods in the Toda case, and helps to explain the structure of the latter

Supersymmetric Boundaries and Junctions in Four Dimensions

We make a comprehensive study of (rigid) N=1 supersymmetric sigma-models with general K\"ahler potentials K and superpotentials w on four-dimensional space-times with boundaries. We determine the minimal (non-supersymmetric) boundary terms one must add to the standard bulk action to make it off-shell invariant under half the supersymmetries without imposing any boundary conditions. Susy boundary conditions do arise from the variational principle when studying the dynamics. Upon including an additional boundary action that depends on an arbitrary real boundary potential B one can generate very general susy boundary conditions. We show that for any set of susy boundary conditions that define a Lagrangian submanifold of the K\"ahler manifold, an appropriate boundary potential B can be found. Thus the non-linear sigma-model on a manifold with boundary is characterised by the tripel (K,B,w). We also discuss the susy coupling to new boundary superfields and generalize our results to supersymmetric junctions between completely different susy sigma-models, living on adjacent domains and interacting through a "permeable" wall. We obtain the supersymmetric matching conditions that allow us to couple models with different K\"ahler potentials and superpotentials on each side of the wall.Comment: 38 pages, 1 figur

Comments on Supersymmetric Vector and Matrix Models

Some results in random matrices are generalized to supermatrices, in particular supermatrix integration is reduced to an integration over the eigenvalues and the resulting volume element is shown to be equivalent to a one dimensional Coulomb gas of both positive and negative charges.It is shown that,for polynomial potentials, after removing the instability due to the annihilation of opposite charges, supermatrix models are indistinguishable from ordinary matrix models, in agreement with a recent result by Alvarez-Gaume and Manes. It is pointed out however that this may not be true for more general potentials such as for instance the supersymmetric generalization of the Penner model.Comment: 6 page

Structure and Growth of Core–shell Nanoprecipitates in Al–Er–Sc–Zr–V–Si High-temperature Alloys

Lightweight Sc-containing aluminum alloys exhibit superior mechanical performance at high temperatures due to core–shell, L12-ordered trialuminide nanoprecipitates. In this study, the structure of these nanoprecipitates was studied, using different transmission electron microscopy (TEM) techniques, for an Al–Er– Sc–Zr–V–Si alloy that was subjected to a two-stage overaging heat treatment. Energy-dispersive X-ray spectroscopy of the spherical Al3(Sc, Zr, Er ,V) nanoprecipitates revealed a core–shell structure with an Sc- and Er-enriched core and a Zr-enriched shell, without a clear V outer shell. This structure is stable up to 72% of the absolute melting temperature of Al for extended periods of time. High-angle annular dark-field scanning TEM was used to image the {100} planes of the nanoprecipitates, demonstrating a homogeneous L12-ordered superlattice structure for the entire nanoprecipitates, despite the variations in the concentrations of solute atoms within the unit cells. A possible growth path and compositional trajectory for these nanoprecipitates was proposed using high-resolution TEM observations, where different rod-like structural defects were detected, which are considered to be precursors to the spherical L12-ordered nanoprecipitates. It is also hypothesized that the structural defects could consist of segregated Si; however, this was not possible to verify with HAADF-STEM because of the small differences in Al and Si atomic numbers. The results herein allow a better understanding of how the Al–Sc alloys’ core–shell nanoprecipitates form and evolve temporally, thereby providing a better physical picture for future atomistic structural mappings and simulations