379 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 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
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
Integrability in SFT and new representation of KP tau-function
We are investigating the properties of vacuum and boundary states in the CFT
of free bosons under the conformal transformation. We show that transformed
vacuum (boundary state) is given in terms of tau-functions of dispersionless KP
(Toda) hierarchies. Applications of this approach to string field theory is
considered. We recognize in Neumann coefficients the matrix of second
derivatives of tau-function of dispersionless KP and identify surface states
with the conformally transformed vacuum of free field theory.Comment: 25 pp, LaTeX, reference added in the Section 3.
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
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
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