470 research outputs found
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.
A Comparison of Supersymmetry Breaking and Mediation Mechanisms
We give a unified treatment of different models of supersymmetry breaking and
mediation from a four dimensional effective field theory standpoint. In
particular a comparison between GMSB and various gravity mediated versions of
SUSY breaking shows that, once the former is embedded within a SUGRA framework,
there is no particular advantage to that mechanism from the point of view of
FCNC suppression. We point out the difficulties of all these scenarios - in
particular the cosmological modulus problem. We end with a discussion of
possible string theory realizations.Comment: Added clarifications and references, 20 page
Dimensional reduction from entanglement in Minkowski space
Using a quantum field theoretic setting, we present evidence for dimensional
reduction of any sub-volume of Minkowksi space. First, we show that correlation
functions of a class of operators restricted to a sub-volume of D-dimensional
Minkowski space scale as its surface area. A simple example of such area
scaling is provided by the energy fluctuations of a free massless quantum field
in its vacuum state. This is reminiscent of area scaling of entanglement
entropy but applies to quantum expectation values in a pure state, rather than
to statistical averages over a mixed state. We then show, in a specific case,
that fluctuations in the bulk have a lower-dimensional representation in terms
of a boundary theory at high temperature.Comment: 9 pages, changes to presentation, some content corrections, version
published in JHE
The Problem of Time and Quantum Black Holes
We discuss the derivation of the so-called semi-classical equations for both
mini-superspace and dilaton gravity. We find that there is no systematic
derivation of a semi-classical theory in which quantum mechanics is formulated
in a space-time that is a solution of Einstein's equation, with the expectation
value of the matter stress tensor on the right-hand side. The issues involved
are related to the well-known problems associated with the interpretation of
the Wheeler-deWitt equation in quantum gravity, including the problem of time.
We explore the de Broglie-Bohm interpretation of quantum mechanics (and field
theory) as a way of spontaneously breaking general covariance, and thereby
giving meaning to the equations that many authors have been using to analyze
black hole evaporation. We comment on the implications for the ``information
loss" problem.Comment: 30 pages, COLO-HEP-33
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
Thermodynamics and area in Minkowski space: Heat capacity of entanglement
Tracing over the degrees of freedom inside (or outside) a sub-volume V of
Minkowski space in a given quantum state |psi>, results in a statistical
ensemble described by a density matrix rho. This enables one to relate quantum
fluctuations in V when in the state |psi>, to statistical fluctuations in the
ensemble described by rho. These fluctuations scale linearly with the surface
area of V. If V is half of space, then rho is the density matrix of a canonical
ensemble in Rindler space. This enables us to `derive' area scaling of
thermodynamic quantities in Rindler space from area scaling of quantum
fluctuations in half of Minkowski space. When considering shapes other than
half of Minkowski space, even though area scaling persists, rho does not have
an interpretation as a density matrix of a canonical ensemble in a curved, or
geometrically non-trivial, background.Comment: 17 page
Semiclassical Approach to Black Hole Evaporation
Black hole evaporation may lead to massive or massless remnants, or naked
singularities. This paper investigates this process in the context of two quite
different two dimensional black hole models. The first is the original CGHS
model, the second is another two dimensional dilaton-gravity model, but with
properties much closer to physics in the real, four dimensional, world.
Numerical simulations are performed of the formation and subsequent evaporation
of black holes and the results are found to agree qualitatively with the
exactly solved modified CGHS models, namely that the semiclassical
approximation breaks down just before a naked singularity appears.Comment: 15 pages, PUPT-1340, harvmac, 11 figures available on reques
Positive Energy Theorem and Supersymmetry in Exactly Solvable Quantum-Corrected 2D Dilaton-Gravity
Extending the work of Park and Strominger, we prove a positive energy theorem
for the exactly solvable quantum-corrected 2D dilaton gravity theories. The
positive energy functional we construct is shown to be unique (within a
reasonably broad class of such functionals). For field configurations
asymptotic to the LDV we show that this energy functional (if defined on a
space-like surface) yields the usual (classical) definition of the ADM mass
{\it plus a certain ``quantum"-correction. If defined on a null surface the
energy functional yields the Bondi mass. The latter is evaluated careflly and
applied to the RST shock-wave scenario where it is shown to behave as
physically expected. Motivated by the existence of a positivity theorem we
construct manifestly supersymmetric (semiclassical) extensions of these
quantum-corrected dilaton-gravity theories.Comment: 30 pages, significantly revised and extended: in particular, the
uniqueness of the positive energy functional is proven and the conditions are
made more precise. The functional is shown to lead to satisfactory ADM and
Bondi masses whose properties are studied in detail. The Bondi mass is
evaluated explicitly for the RST shockwave scenari
Numerical Analysis of Black Hole Evaporation
Black hole formation/evaporation in two-dimensional dilaton gravity can be
described, in the limit where the number of matter fields becomes large, by
a set of second-order partial differential equations. In this paper we solve
these equations numerically. It is shown that, contrary to some previous
suggestions, black holes evaporate completely a finite time after formation. A
boundary condition is required to evolve the system beyond the naked
singularity at the evaporation endpoint. It is argued that this may be
naturally chosen so as to restore the system to the vacuum. The analysis also
applies to the low-energy scattering of -wave fermions by four-dimensional
extremal, magnetic, dilatonic black holes.Comment: 10 pages, 9 figures in separate uuencoded fil
On a Modification of the Boundary State Formalism in Off-shell String Theory
We examine the application of boundary states in computing amplitudes in
off-shell open string theory. We find a straightforward generalization of
boundary state which produces the correct matrix elements with on-shell closed
string states.Comment: Latex, 10 pages, refs added, minor typos correcte
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