61 research outputs found
Gauge Invariant Matrix Model for the \^A-\^D-\^E Closed Strings
The models of triangulated random surfaces embedded in (extended) Dynkin
diagrams are formulated as a gauge-invariant matrix model of Weingarten type.
The double scaling limit of this model is described by a collective field
theory with nonpolynomial interaction.
The propagator in this field theory is essentially two-loop correlator in the
corresponding string theory.Comment: 9 pages, SPhT/92-09
Field Theory of Open and Closed Strings with Discrete Target Space
We study a -invariant vector+matrix chain with the color structure of a
lattice gauge theory with quarks and interpret it as a theory of open andclosed
strings with target space . The string field theory is constructed as a
quasiclassical expansion for the Wilson loops and lines in this model. In a
particular parametrization this is a theory of two scalar massless fields
defined in the half-space . The extra dimension
is related to the longitudinal mode of the strings. The topology-changing
string interactions are described by a local potential. The closed string
interaction is nonzero only at boundary while the open string
interaction falls exponentially with .Comment: 15 pages, harvmac. no figures; some typos corrected and a reference
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Loop Gas Model for Open Strings
The open string with one-dimensional target space is formulated in terms of
an SOS, or loop gas, model on a random surface. We solve an integral equation
for the loop amplitude with Dirichlet and Neumann boundary conditions imposed
on different pieces of its boundary. The result is used to calculate the mean
values of order and disorder operators, to construct the string propagator and
find its spectrum of excitations. The latter is not sensible neither to the
string tension \L nor to the mass of the ``quarks'' at the ends of the
string. As in the case of closed strings, the SOS formulation allows to
construct a Feynman diagram technique for the string interaction amplitudes
Feynman rules for string field theories with discrete target space
We derive a minimal set of Feynman rules for the loop amplitudes in unitary
models of closed strings, whose target space is a simply laced (extended)
Dynkin diagram. The string field Feynman graphs are composed of propagators,
vertices (including tadpoles) of all topologies, and leg factors for the
macroscopic loops. A vertex of given topology factorizes into a fusion
coefficient for the matter fields and an intersection number associated with
the corresponding punctured surface. As illustration we obtain explicit
expressions for the genus-one tadpole and the genus-zero four-loop amplitude.Comment: 19 pages, harvmac, 4 uuencoded figures included using epsf. A missing
term added to the expression for the genus-one tadpole and Fig.3 modified
correspondingl
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
LOOP SPACE HAMILTONIAN FOR OPEN STRINGS
We construct a string field Hamiltonian describing the dynamics of open and
closed strings with effective target-space dimension . In order to do
so, we first derive the Dyson-Schwinger equations for the underlying large
vector+matrix model and formulate them as a set of constraints satisfying
decoupled Virasoro and U(1) current algebras. The Hamiltonian consists of a
bulk and a boundary term having different scaling dimensions. The time
parameters corresponding to the two terms are interpreted from the the point of
view of the fractal geometry of the world surface.Comment: 15 pages, plain tex, harvmac, no figure
Non-Rational 2D Quantum Gravity: I. World Sheet CFT
We address the problem of computing the tachyon correlation functions in
Liouville gravity with generic (non-rational) matter central charge c<1. We
consider two variants of the theory. The first is the conventional one in which
the effective matter interaction is given by the two matter screening charges.
In the second variant the interaction is defined by the Liouville dressings of
the non-trivial vertex operator of zero dimension. This particular deformation,
referred to as "diagonal'', is motivated by the comparison with the discrete
approach, which is the subject of a subsequent paper. In both theories we
determine the ground ring of ghost zero physical operators by computing its OPE
action on the tachyons and derive recurrence relations for the tachyon bulk
correlation functions. We find 3- and 4-point solutions to these functional
equations for various matter spectra. In particular, we find a closed
expression for the 4-point function of order operators in the diagonal theory.Comment: TEX-harvmac, revised version to appear in Nuclear Physics
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
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.
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