680 research outputs found
Character Expansion Methods for Matrix Models of Dually Weighted Graphs
We consider generalized one-matrix models in which external fields allow
control over the coordination numbers on both the original and dual lattices.
We rederive in a simple fashion a character expansion formula for these models
originally due to Itzykson and Di Francesco, and then demonstrate how to take
the large N limit of this expansion. The relationship to the usual matrix model
resolvent is elucidated. Our methods give as a by-product an extremely simple
derivation of the Migdal integral equation describing the large limit of
the Itzykson-Zuber formula. We illustrate and check our methods by analyzing a
number of models solvable by traditional means. We then proceed to solve a new
model: a sum over planar graphs possessing even coordination numbers on both
the original and the dual lattice. We conclude by formulating equations for the
case of arbitrary sets of even, self-dual coupling constants. This opens the
way for studying the deep problem of phase transitions from random to flat
lattices.Comment: 22 pages, harvmac.tex, pictex.tex. All diagrams written directly into
the text in Pictex commands. (Two minor math typos corrected.
Acknowledgements added.
On the connection between Quantum Mechanics and the geometry of two-dimensional strings
On the basis of an area-preserving symmetry in the phase space of a
one-dimensional matrix model - believed to describe two-dimensional string
theory in a black-hole background which also allows for space-time foam - we
give a geometric interpretation of the fact that two-dimensional stringy black
holes are consistent with conventional quantum mechanics due to the infinite
gauged `W-hair' property that characterises them.Comment: 19 page
The Origin of Space-Time as Symmetry Breaking in String Theory
Physics in the neighbourhood of a space-time metric singularity is described
by a world-sheet topological gauge field theory which can be represented as a
twisted superconformal Wess-Zumino model with a bosonic symmetry. The measurable -hair associated with the
singularity is associated with Wilson loop integrals around gauge defects. The
breaking of
is associated with expectation values for open Wilson lines that
make the metric non-singular away from the singularity. This symmetry breaking
is accompanied by massless discrete `tachyon' states that appear as leg poles
in -matrix elements. The triviality of the -matrix in the high-energy
limit of the string model, after renormalisation by the leg pole factors,
is due to the restoration of double -symmetry at the singularity.Comment: 13 page
Quantum Mechanics and Black Holes in Four-Dimensional String Theory
In previous papers we have shown how strings in a two-dimensional target
space reconcile quantum mechanics with general relativity, thanks to an
infinite set of conserved quantum numbers, ``W-hair'', associated with
topological soliton-like states. In this paper we extend these arguments to
four dimensions, by considering explicitly the case of string black holes with
radial symmetry. The key infinite-dimensional W-symmetry is associated with the
coset structure of the dilaton-graviton sector that is a
model-independent feature of spherically symmetric four-dimensional strings.
Arguments are also given that the enormous number of string {\it discrete
(topological)} states account for the maintenance of quantum coherence during
the (non-thermal) stringy evaporation process, as well as quenching the large
Hawking-Bekenstein entropy associated with the black hole. Defining the latter
as the measure of the loss of information for an observer at infinity, who -
ignoring the higher string quantum numbers - keeps track only of the classical
mass,angular momentum and charge of the black hole, one recovers the familiar a
quadratic dependence on the black-hole mass by simple counting arguments on the
asymptotic density of string states in a linear-dilaton background.Comment: 18 page
String Theory Modifies Quantum Mechanics
We argue that the light particles in string theory obey an effective quantum
mechanics modified by the inclusion of a quantum-gravitational friction term,
induced by unavoidable couplings to unobserved massive string states in the
space-time foam. This term is related to the -symmetries that couple light
particles to massive solitonic string states in black hole backgrounds, and has
a formal similarity to simple models of environmental quantum friction. It
increases apparent entropy, and may induce the wave functions of macroscopic
systems to collapse.Comment: 18 pages, CERN-6595/9
Robust Limits on Lorentz Violation from Gamma-Ray Bursts
We constrain the possibility of a non-trivial refractive index in free space
corresponding to an energy-dependent velocity of light: c(E) \simeq c_0 (1 -
E/M), where M is a mass scale that might represent effect of
quantum-gravitational space-time foam, using the arrival times of sharp
features observed in the intensities of radiation with different energies from
a large sample of gamma-ray bursters (GRBs) with known redshifts. We use
wavelet techniques to identify genuine features, which we confirm in
simulations with artificial added noise. Using the weighted averages of the
time-lags calculated using correlated features in all the GRB light curves, we
find a systematic tendency for more energetic photons to arrive earlier.
However, there is a very strong correlation between the parameters
characterizing an intrinsic time-lag at the source and a distance-dependent
propagation effect. Moreover, the significance of the earlier arrival times is
less evident for a subsample of more robust spectral structures. Allowing for
intrinsic stochastic time-lags in these features, we establish a statistically
robust lower limit: M > 0.9x10^{16} GeV on the scale of violation of Lorentz
invariance.Comment: 18 pages, 4 eps figure
Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy
We present three holographic constructions of fractional quantum Hall effect
(FQHE) via string theory. The first model studies edge states in FQHE using
supersymmetric domain walls in N=6 Chern-Simons theory. We show that D4-branes
wrapped on CP^1 or D8-branes wrapped on CP^3 create edge states that shift the
rank or the level of the gauge group, respectively. These holographic edge
states correctly reproduce the Hall conductivity. The second model presents a
holographic dual to the pure U(N)_k (Yang-Mills-)Chern-Simons theory based on a
D3-D7 system. Its holography is equivalent to the level-rank duality, which
enables us to compute the Hall conductivity and the topological entanglement
entropy. The third model introduces the first string theory embedding of
hierarchical FQHEs, using IIA string on C^2/Z_n.Comment: 36 pages, 6 figures; v2: with an improved derivation of Hall
conductivity in section 3.2, typo corrections, and additional references; v3:
explanations and comments adde
On the Evaporation of Black Holes in String Theory
We show that, in string theory, the quantum evaporation and decay of black
holes in two-dimensional target space is related to imaginary parts in
higher-genus string amplitudes. These arise from the regularisation of modular
infinities due to the sum over world-sheet configurations, that are known to
express the instabilities of massive string states in general, and are not
thermal in character. The absence of such imaginary parts in the matrix model
limit confirms that the latter constitutes the final stage of the evaporation
process, at least in perturbation theory. Our arguments appear to be quite
generic, related only to the summation over world-sheet surfaces, and hence
should also apply to higher-dimensional target spaces.Comment: 17 page
Notes on D-branes in 2D Type 0 String Theory
In this paper we construct complete macroscopic operators in two dimensional
type 0 string theory. They represent D-branes localized in the time direction.
We give another equivalent description of them as deformed Fermi surfaces. We
also discuss a continuous array of such D-branes and show that it can be
described by a matrix model with a deformed potential. For appropriate values
of parameters, we find that it has an additional new sector hidden inside its
strongly coupled region.Comment: harvmac, 18 pages, 2 figures, references adde
Lowest-Landau-level theory of the quantum Hall effect: the Fermi-liquid-like state
A theory for a Fermi-liquid-like state in a system of charged bosons at
filling factor one is developed, working in the lowest Landau level. The
approach is based on a representation of the problem as fermions with a system
of constraints, introduced by Pasquier and Haldane (unpublished). This makes
the system a gauge theory with gauge algebra W_infty. The low-energy theory is
analyzed based on Hartree-Fock and a corresponding conserving approximation.
This is shown to be equivalent to introducing a gauge field, which at long
wavelengths gives an infinite-coupling U(1) gauge theory, without a
Chern-Simons term. The system is compressible, and the Fermi-liquid properties
are similar, but not identical, to those in the previous U(1) Chern-Simons
fermion theory. The fermions in the theory are effectively neutral but carry a
dipole moment. The density-density response, longitudinal conductivity, and the
current density are considered explicitly.Comment: 32 pages, revtex multicol
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