31 research outputs found
A Comment on Quantum Distribution Functions and the OSV Conjecture
Using the attractor mechanism and the relation between the quantization of
and topological strings on a Calabi Yau threefold we define a
map from BPS black holes into coherent states. This map allows us to represent
the Bekenstein-Hawking-Wald entropy as a quantum distribution function on the
phase space . This distribution function is a mixed
Husimi/anti-Husimi distribution corresponding to the different normal ordering
prescriptions for the string coupling and deviations of the complex structure
moduli. From the integral representation of this distribution function in terms
of the Wigner distribution we recover the Ooguri-Strominger-Vafa (OSV)
conjecture in the region "at infinity" of the complex structure moduli space.
The physical meaning of the OSV corrections are briefly discussed in this
limit.Comment: 27 pages. v2:reference and footnote adde
Schroedingers equation with gauge coupling derived from a continuity equation
We consider a statistical ensemble of particles of mass m, which can be
described by a probability density \rho and a probability current \vec{j} of
the form \rho \nabla S/m. The continuity equation for \rho and \vec{j} implies
a first differential equation for the basic variables \rho and S. We further
assume that this system may be described by a linear differential equation for
a complex state variable \chi. Using this assumptions and the simplest possible
Ansatz \chi(\rho,S) Schroedingers equation for a particle of mass m in an
external potential V(q,t) is deduced. All calculations are performed for a
single spatial dimension (variable q) Using a second Ansatz \chi(\rho,S,q,t)
which allows for an explict q,t-dependence of \chi, one obtains a generalized
Schroedinger equation with an unusual external influence described by a
time-dependent Planck constant. All other modifications of Schroeodingers
equation obtained within this Ansatz may be eliminated by means of a gauge
transformation. Thus, this second Ansatz may be considered as a generalized
gauging procedure. Finally, making a third Ansatz, which allows for an
non-unique external q,t-dependence of \chi, one obtains Schroedingers equation
with electromagnetic potentials \vec{A}, \phi in the familiar gauge coupling
form. A possible source of the non-uniqueness is pointed out.Comment: 25 pages, no figure
S-branes and (Anti-)Bubbles in (A)dS Space
We describe the construction of new locally asymptotically (A)dS geometries
with relevance for the AdS/CFT and dS/CFT correspondences. Our approach is to
obtain new solutions by analytically continuing black hole solutions. A basic
consideration of the method of continuation indicates that these solutions come
in three classes: S-branes, bubbles and anti-bubbles. A generalization to
spinning or twisted solutions can yield spacetimes with complicated horizon
structures. Interestingly enough, several of these spacetimes are nonsingular.Comment: 35 pages, 12 figures. V2: JHEP style, expanded reference
Sequences of Bubbles and Holes: New Phases of Kaluza-Klein Black Holes
We construct and analyze a large class of exact five- and six-dimensional
regular and static solutions of the vacuum Einstein equations. These solutions
describe sequences of Kaluza-Klein bubbles and black holes, placed alternately
so that the black holes are held apart by the bubbles. Asymptotically the
solutions are Minkowski-space times a circle, i.e. Kaluza-Klein space, so they
are part of the (\mu,n) phase diagram introduced in hep-th/0309116. In
particular, they occupy a hitherto unexplored region of the phase diagram,
since their relative tension exceeds that of the uniform black string. The
solutions contain bubbles and black holes of various topologies, including
six-dimensional black holes with ring topology S^3 x S^1 and tuboid topology
S^2 x S^1 x S^1. The bubbles support the S^1's of the horizons against
gravitational collapse. We find two maps between solutions, one that relates
five- and six-dimensional solutions, and another that relates solutions in the
same dimension by interchanging bubbles and black holes. To illustrate the
richness of the phase structure and the non-uniqueness in the (\mu,n) phase
diagram, we consider in detail particular examples of the general class of
solutions.Comment: 71 pages, 22 figures, v2: Typos fixed, comment added in sec. 5.
Epistemic and Ontic Quantum Realities
Quantum theory has provoked intense discussions about its interpretation since its pioneer days. One of the few scientists who have been continuously engaged in this development from both physical and philosophical perspectives is Carl Friedrich von Weizsaecker. The questions he posed were and are inspiring for many, including the authors of this contribution. Weizsaecker developed Bohr's view of quantum theory as a theory of knowledge. We show that such an epistemic perspective can be consistently complemented by Einstein's ontically oriented position
The Fuzzy Disc
We introduce a finite dimensional matrix model approximation to the algebra
of functions on a disc based on noncommutative geometry. The algebra is a
subalgebra of the one characterizing the noncommutative plane with a * product
and depends on two parameters N and theta. It is composed of functions which
decay exponentially outside a disc. In the limit in which the size of the
matrices goes to infinity and the noncommutativity parameter goes to zero the
disc becomes sharper. We introduce a Laplacian defined on the whole algebra and
calculate its eigenvalues. We also calculate the two--points correlation
function for a free massless theory (Green's function). In both cases the
agreement with the exact result on the disc is very good already for relatively
small matrices. This opens up the possibility for the study of field theories
on the disc with nonperturbative methods. The model contains edge states, a
fact studied in a similar matrix model independently introduced by
Balachandran, Gupta and Kurkcuoglu.Comment: 17 pages, 8 figures, references added and correcte