57 research outputs found
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
Boundary changing operators in the O(n) matrix model
We continue the study of boundary operators in the dense O(n) model on the
random lattice. The conformal dimension of boundary operators inserted between
two JS boundaries of different weight is derived from the matrix model
description. Our results are in agreement with the regular lattice findings. A
connection is made between the loop equations in the continuum limit and the
shift relations of boundary Liouville 3-points functions obtained from Boundary
Ground Ring approach.Comment: 31 pages, 4 figures, Introduction and Conclusion improve
Complex Curve of the Two Matrix Model and its Tau-function
We study the hermitean and normal two matrix models in planar approximation
for an arbitrary number of eigenvalue supports. Its planar graph interpretation
is given. The study reveals a general structure of the underlying analytic
complex curve, different from the hyperelliptic curve of the one matrix model.
The matrix model quantities are expressed through the periods of meromorphic
generating differential on this curve and the partition function of the
multiple support solution, as a function of filling numbers and coefficients of
the matrix potential, is shown to be the quasiclassical tau-function. The
relation to softly broken N=1 supersymmetric Yang-Mills theories is discussed.
A general class of solvable multimatrix models with tree-like interactions is
considered.Comment: 36 pages, 10 figures, TeX; final version appeared in special issue of
J.Phys. A on Random Matrix Theor
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
Some New/Old Approaches to QCD
This is a talk delivered at the Meeting on Integrable Quantum Field Theories,
Villa Olmo and at STRINGS 1992, Rome, September 1992. I discuss some recent
attempts to revive two old ideas regarding an analytic approach to QCD-the
development of a string representation of the theory and the large N limit of
QCD.Comment: 20 page
Integrable flows in c=1 string theory
In these notes we review the method to construct integrable deformations of
the compactified c=1 bosonic string theory by primary fields (momentum or
winding modes), developed recently in collaboration with S. Alexandrov and V.
Kazakov. The method is based on the formulation of the string theory as a
matrix model. The flows generated by either momentum or winding modes (but not
both) are integrable and satisfy the Toda lattice hierarchy.Comment: sect.1 extended and typos correcte
Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory
New loop equations for all genera in non-critical string
theory are constructed. Our loop equations include two types of loops, loops
with all Ising spins up (+ loops) and those with all spins down ( loops).
The loop equations generate an algebra which is a certain extension of
algebra and are equivalent to the constraints derived before in the
matrix-model formulation of 2d gravity. Application of these loop equations to
construction of Hamiltonian for string field theory is
considered.Comment: 21 pages, LaTex file, no figure
T-Duality Transformation and Universal Structure of Non-Critical String Field Theory
We discuss a T-duality transformation for the c=1/2 matrix model for the
purpose of studying duality transformations in a possible toy example of
nonperturbative frameworks of string theory. Our approach is to first
investigate the scaling limit of the Schwinger-Dyson equations and the
stochastic Hamiltonian in terms of the dual variables and then compare the
results with those using the original spin variables. It is shown that the
c=1/2 model in the scaling limit is T-duality symmetric in the sphere
approximation. The duality symmetry is however violated when the higher-genus
effects are taken into account, owing to the existence of global Z_2 vector
fields corresponding to nontrivial homology cycles. Some universal properties
of the stochastic Hamiltonians which play an important role in discussing the
scaling limit and have been discussed in a previous work by the last two
authors are refined in both the original and dual formulations. We also report
a number of new explicit results for various amplitudes containing macroscopic
loop operators.Comment: RevTex, 46 pages, 5 eps figure
A Remark on the Renormalization Group Equation for the Penner Model
It is possible to extract values for critical couplings and gamma_string in
matrix models by deriving a renormalization group equation for the variation of
the of the free energy as the size N of the matrices in the theory is varied.
In this paper we derive a ``renormalization group equation'' for the Penner
model by direct differentiation of the partition function and show that it
reproduces the correct values of the critical coupling and gamma_string and is
consistent with the logarithmic corrections present for g=0,1.Comment: LaTeX, 5 pages, LPTHE-Orsay-94-5
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