98 research outputs found
Towards Quantum Cosmology without Singularities
In this paper we investigate the vanishing of cosmological singularities by
quantization. Starting from a 5d Kaluza--Klein approach we quantize, as a first
step, the non--spherical metric part and the dilaton field. These fields which
are classically singular become smooth after quantization. In addition, we
argue that the incorporation of non perturbative quantum corrections form a
dilaton potential. Technically, the procedure corresponds to the quantization
of 2d dilaton gravity and we discuss several models. From the 4d point of view
this procedure is a semiclassical approach where only the dilaton and moduli
matter fields are quantized.Comment: 9 pages, 2 figures, Latex, epsfig.sty, epsf.te
Effects of Synaptic and Myelin Plasticity on Learning in a Network of Kuramoto Phase Oscillators
Models of learning typically focus on synaptic plasticity. However, learning
is the result of both synaptic and myelin plasticity. Specifically, synaptic
changes often co-occur and interact with myelin changes, leading to complex
dynamic interactions between these processes. Here, we investigate the
implications of these interactions for the coupling behavior of a system of
Kuramoto oscillators. To that end, we construct a fully connected,
one-dimensional ring network of phase oscillators whose coupling strength
(reflecting synaptic strength) as well as conduction velocity (reflecting
myelination) are each regulated by a Hebbian learning rule. We evaluate the
behavior of the system in terms of structural (pairwise connection strength and
conduction velocity) and functional connectivity (local and global
synchronization behavior). We find that for conditions in which a system
limited to synaptic plasticity develops two distinct clusters both structurally
and functionally, additional adaptive myelination allows for functional
communication across these structural clusters. Hence, dynamic conduction
velocity permits the functional integration of structurally segregated
clusters. Our results confirm that network states following learning may be
different when myelin plasticity is considered in addition to synaptic
plasticity, pointing towards the relevance of integrating both factors in
computational models of learning.Comment: 39 pages, 15 figures This work is submitted in Chaos: An
Interdisciplinary Journal of Nonlinear Scienc
Quantum Theories of Dilaton Gravity
Quantization of two-dimensional dilaton gravity coupled to conformal matter
is investigated. Working in conformal gauge about a fixed background metric,
the theory may be viewed as a sigma model whose target space is parameterized
by the dilaton and conformal factor . A precise connection is
given between the constraint that the theory be independent of the background
metric and conformal invariance of the resulting sigma model. Although the
action is renormalizable, new coupling constants must be specified at each
order in perturbation theory in order to determine the quantum theory. These
constants may be viewed as initial data for the beta function equations. It is
argued that not all choices of this data correspond to physically sensible
theories of gravity, and physically motivated constraints on the data are
discussed. In particular a recently constructed subclass of initial data which
reduces the full quantum theory to a soluble Liouville-like theory has energies
unbounded from below and thus is unphysical. Possibilities for modifying this
construction so as to avoid this difficulty are briefly discussed.Comment: 20 pages (Major additions made, including 5 pages on the relation
between conformal invariance and background independence.
Brief comments on Jackiw-Teitelboim gravity coupled to Liouville theory
Jackiw-Teitelboim gravity with non-vanishing cosmological constant coupled to
Liouville theory is considered as a non-critical string on dimensional flat
spacetime. It is discussed how the presence of cosmological constant yields
additional constraints on the parameter space of the theory, even when the
conformal anomaly is independent of the cosmological constant. Such constraints
agree with the necessary conditions for the tachyon field to be a primary
--prelogarithmic-- operator of the worldsheet conformal field theory. Thus, the
linearized tachyon field equation allows to impose the diagonal condition for
the interaction term. We analyze the neutralization of the Liouville mode
induced by the coupling to the Jackiw-Teitelboim Lagrangian. The free field
prescription leads to obtain explicit expressions for three-point correlation
functions for the case of vanishing cosmological constant in terms of a product
of Shapiro-Virasoro integrals. This is a consequence of the mentioned
neutralization effect.Comment: 14 pages, no figures. v2 References added. To be published in
Classical and Quantum Gravity. v3 typos correcte
Yukawa Coupling Structure in Intersecting D-brane Models
The structure of Yukawa coupling matrices is investigated in type IIA
T^6/(Z_2 x Z_2) orientifold models with intersecting D-branes. Yukawa coupling
matrices are difficult to be realistic in the conventional models in which the
generation structure emerges by the multiple intersection of D-branes in the
factorized T^6 = T^2 x T^2 x T^2. We study the new type of flavor structure,
where Yukawa couplings are dynamically generated, and show this type of models
lead to nontrivial structures of Yukawa coupling matrices, which can be
realistic.Comment: 9 pages, 2 figure
The Stretched Horizon and Black Hole Complementarity
Three postulates asserting the validity of conventional quantum theory,
semi-classical general relativity and the statistical basis for thermodynamics
are introduced as a foundation for the study of black hole evolution. We
explain how these postulates may be implemented in a ``stretched horizon'' or
membrane description of the black hole, appropriate to a distant observer. The
technical analysis is illustrated in the simplified context of 1+1 dimensional
dilaton gravity. Our postulates imply that the dissipative properties of the
stretched horizon arise from a course graining of microphysical degrees of
freedom that the horizon must possess. A principle of black hole
complementarity is advocated. The overall viewpoint is similar to that
pioneered by 't~Hooft but the detailed implementation is different.Comment: (some misprints in equations have been fixed), 48 pages (including
figures), SU-ITP-93-1
On 'Light' Fermions and Proton Stability in 'Big Divisor' D3/D7 Swiss Cheese Phenomenology
Building up on our earlier work [1,2], we show the possibility of generating
"light" fermion mass scales of MeV-GeV range (possibly related to first two
generations of quarks/leptons) as well as eV (possibly related to first two
generations of neutrinos) in type IIB string theory compactified on
Swiss-Cheese orientifolds in the presence of a mobile space-time filling
D3-$brane restricted to (in principle) stacks of fluxed D7-branes wrapping the
"big" divisor \Sigma_B. This part of the paper is an expanded version of the
latter half of section 3 of a published short invited review [3] written up by
one of the authors [AM]. Further, we also show that there are no SUSY GUT-type
dimension-five operators corresponding to proton decay, as well as estimate the
proton lifetime from a SUSY GUT-type four-fermion dimension-six operator to be
10^{61} years. Based on GLSM calculations in [1] for obtaining the geometric
Kaehler potential for the "big divisor", using further the Donaldson's
algorithm, we also briefly discuss in the first of the two appendices,
obtaining a metric for the Swiss-Cheese Calabi-Yau used, that becomes Ricci
flat in the large volume limit.Comment: v2: 1+25 pages, Title modified and text thoroughly expanded including
a brief discussion on obtaining Ricci-flat Swiss Cheese Calabi-Yau metrics
using the Donaldson's algorithm, references added, to appear in EPJ
Dilaton Quantum Cosmology in Two Dimensions
We consider a renormalizable two-dimensional model of dilaton gravity coupled
to a set of conformal fields as a toy model for quantum cosmology. We discuss
the cosmological solutions of the model and study the effect of including the
backreaction due to quantum corrections. As a result, when the matter density
is below some threshold new singularities form in a weak coupling region, which
suggests that they will not be removed in the full quantum theory. We also
solve the Wheeler-DeWitt equation. Depending on the quantum state of the
Universe, the singularities may appear in a quantum region where the wave
function is not oscillatory, i.e., when there is not a well defined notion of
classical spacetime.Comment: 17 pages, UTTG-28-9
Finite sigma models and exact string solutions with Minkowski signature metric
We consider sigma models with a - dimensional Minkowski
signature target space metric having a covariantly constant null Killing
vector. These models are UV finite. The -dimensional target space metric
can be explicitly determined for a class of supersymmetric sigma models with
-dimensional `transverse' part of the target space being homogeneous
K\"ahler. The corresponding `transverse' sub-theory is an supersymmetric
sigma model with the exact \gb-function coinciding with its one-loop
expression. For example, the finite model has supersymmetric sigma
model as its `transverse' part. Moreover, there exists a non-trivial dilaton
field such that the Weyl invariance conditions are also satisfied, i.e. the
resulting models correspond to string vacua. Generic solutions are represented
in terms of the RG flow in `transverse' theory. We suggest a possible
application of the constructed Weyl invariant sigma models to quantisation of
gravity. They may be interpreted as `effective actions' of the quantum
dilaton gravity coupled to a (non-conformal) -dimensional `matter'
theory. The conformal factor of the metric and `dilaton' are
identified with the light cone coordinates of the - dimensional sigma
model.Comment: 24 pages, harvmac, Imperial/TP/92-93/
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