409 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
On Kernel Formulas and Dispersionless Hirota Equations
We rederive dispersionless Hirota equations of the dispersionless Toda
hierarchy from the method of kernel formula provided by Carroll and Kodama. We
then apply the method to derive dispersionless Hirota equations of the extended
dispersionless BKP(EdBKP) hierarchy proposed by Takasaki. Moreover, we verify
associativity equations (WDVV equations) in the EdBKP hierarchy from
dispersionless Hirota equations and give a realization of associative algebra
with structure constants expressed in terms of residue formula.Comment: 30 pages, minor corrections, references adde
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
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
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
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
Growth of fat slits and dispersionless KP hierarchy
A "fat slit" is a compact domain in the upper half plane bounded by a curve
with endpoints on the real axis and a segment of the real axis between them. We
consider conformal maps of the upper half plane to the exterior of a fat slit
parameterized by harmonic moments of the latter and show that they obey an
infinite set of Lax equations for the dispersionless KP hierarchy. Deformation
of a fat slit under changing a particular harmonic moment can be treated as a
growth process similar to the Laplacian growth of domains in the whole plane.
This construction extends the well known link between solutions to the
dispersionless KP hierarchy and conformal maps of slit domains in the upper
half plane and provides a new, large family of solutions.Comment: 26 pages, 6 figures, typos correcte
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