969 research outputs found
Rational Theories of 2D Gravity from the Two-Matrix Model
The correspondence claimed by M. Douglas, between the multicritical regimes
of the two-matrix model and 2D gravity coupled to (p,q) rational matter field,
is worked out explicitly. We found the minimal (p,q) multicritical potentials
U(X) and V(Y) which are polynomials of degree p and q, correspondingly. The
loop averages W(X) and \tilde W(Y) are shown to satisfy the Heisenberg
relations {W,X} =1 and {\tilde W,Y}=1 and essentially coincide with the
canonical momenta P and Q. The operators X and Y create the two kinds of
boundaries in the (p,q) model related by the duality (p,q) - (q,p). Finally, we
present a closed expression for the two two-loop correlators and interpret its
scaling limit.Comment: 24 pages, preprint CERN-TH.6834/9
Two Dimensional QCD as a String Theory
I explore the possibility of finding an equivalent string representation of
two dimensional QCD. I develop the large N expansion of the
partition function on an arbitrary two dimensional Euclidean manifold. If this
is related to a two-dimensional string theory then many of the coefficients of
the expansion must vanish. This is shown to be true to all orders,
giving strong evidence for the existence of a string representation.Comment: 24 page
Scattering of Long Folded Strings and Mixed Correlators in the Two-Matrix Model
We study the interactions of Maldacena's long folded strings in
two-dimensional string theory. We find the amplitude for a state containing two
long folded strings to come and go back to infinity. We calculate this
amplitude both in the worldsheet theory and in the dual matrix model, the
Matrix Quantum Mechanics. The matrix model description allows to evaluate the
amplitudes involving any number of long strings, which are given by the mixed
trace correlators in an effective two-matrix model.Comment: 39 pages, 6 figure
Bulk correlation functions in 2D quantum gravity
We compute bulk 3- and 4-point tachyon correlators in the 2d Liouville
gravity with non-rational matter central charge c<1, following and comparing
two approaches. The continuous CFT approach exploits the action on the tachyons
of the ground ring generators deformed by Liouville and matter ``screening
charges''. A by-product general formula for the matter 3-point OPE structure
constants is derived. We also consider a ``diagonal'' CFT of 2D quantum
gravity, in which the degenerate fields are restricted to the diagonal of the
semi-infinite Kac table. The discrete formulation of the theory is a
generalization of the ADE string theories, in which the target space is the
semi-infinite chain of points.Comment: 14 pages, 2 figure
Quasiperiodic Solutions of the Fibre Optics Coupled Nonlinear Schr{\"o}dinger Equations
We consider travelling periodical and quasiperiodical waves in single mode
fibres, with weak birefringence and under the action of cross-phase modulation.
The problem is reduced to the ``1:2:1" integrable case of the two-particle
quartic potential. A general approach for finding elliptic solutions is given.
New solutions which are associated with two-gap Treibich-Verdier potentials are
found. General quasiperiodic solutions are given in terms of two dimensional
theta functions with explicit expressions for frequencies in terms of theta
constants. The reduction of quasiperiodic solutions to elliptic functions is
discussed.Comment: 24 page
Boundary operators in the O(n) and RSOS matrix models
We study the new boundary condition of the O(n) model proposed by Jacobsen
and Saleur using the matrix model. The spectrum of boundary operators and their
conformal weights are obtained by solving the loop equations. Using the
diagrammatic expansion of the matrix model as well as the loop equations, we
make an explicit correspondence between the new boundary condition of the O(n)
model and the "alternating height" boundary conditions in RSOS model.Comment: 29 pages, 4 figures; version to appear in JHE
The model on a random surface: critical points and large order behaviour
In this article we report a preliminary investigation of the large limit
of a generalized one-matrix model which represents an symmetric model on
a random lattice. The model on a regular lattice is known to be critical only
for . This is the situation we shall discuss also here, using
steepest descent. We first determine the critical and multicritical points,
recovering in particular results previously obtained by Kostov. We then
calculate the scaling behaviour in the critical region when the cosmological
constant is close to its critical value. Like for the multi-matrix models, all
critical points can be classified in terms of two relatively prime integers
. In the parametrization , integers such that
, the string susceptibility exponent is found to be . When we find that all results agree with those of
the corresponding string models, otherwise they are different.\par We
finally explain how to derive the large order behaviour of the corresponding
topological expansion in the double scaling limit.Comment: 33 page
Correlation Functions in the Multiple Ising Model Coupled to Gravity
The model of p Ising spins coupled to 2d gravity, in the form of a sum over
planar phi-cubed graphs, is studied and in particular the two-point and
spin-spin correlation functions are considered. We first solve a toy model in
which only a partial summation over spin configurations is performed and, using
a modified geodesic distance, various correlation functions are determined. The
two-point function has a diverging length scale associated with it. The
critical exponents are calculated and it is shown that all the standard scaling
relations apply. Next the full model is studied, in which all spin
configurations are included. Many of the considerations for the toy model apply
for the full model, which also has a diverging geometric correlation length
associated with the transition to a branched polymer phase. Using a transfer
function we show that the two-point and spin-spin correlation functions decay
exponentially with distance. Finally, by assuming various scaling relations, we
make a prediction for the critical exponents at the transition between the
magnetized and branched polymer phases in the full model.Comment: 29 pages, LaTeX, uses epsf macro, 5 figure
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