277 research outputs found
Coloring Random Triangulations
We introduce and solve a two-matrix model for the tri-coloring problem of the
vertices of a random triangulation. We present three different solutions: (i)
by orthogonal polynomial techniques (ii) by use of a discrete Hirota bilinear
equation (iii) by direct expansion. The model is found to lie in the
universality class of pure two-dimensional quantum gravity, despite the
non-polynomiality of its potential.Comment: 50 pages, 4 figures, Tex, uses harvmac, eps
Comments on Supersymmetric Vector and Matrix Models
Some results in random matrices are generalized to supermatrices, in
particular supermatrix integration is reduced to an integration over the
eigenvalues and the resulting volume element is shown to be equivalent to a one
dimensional Coulomb gas of both positive and negative charges.It is shown
that,for polynomial potentials, after removing the instability due to the
annihilation of opposite charges, supermatrix models are indistinguishable from
ordinary matrix models, in agreement with a recent result by Alvarez-Gaume and
Manes. It is pointed out however that this may not be true for more general
potentials such as for instance the supersymmetric generalization of the Penner
model.Comment: 6 page
Permutation combinatorics of worldsheet moduli space
52 pages, 21 figures52 pages, 21 figures; minor corrections, "On the" dropped from title, matches published version52 pages, 21 figures; minor corrections, "On the" dropped from title, matches published versio
Topological Landau-Ginzburg Model of Two-Dimensional String Theory
We study a topological Landau-Ginzburg model with superpotential W(X)=X^{-1}.
This is argued to be equivalent to c=1 string theory compactified at the
self-dual radius. We compute the tree-level correlation function of N tachyons
in this theory and show their agreement with matrix-model results. We also
discuss the nature of contact terms, the perturbed superpotential and the flow
of operators in the small phase space. The role of gravitational descendants in
this theory is examined, and the tachyon two-point function in genus 1 is
obtained using a conjectured modification of the gravitational recursion
relations.Comment: 22 pages, harvmac, Mehta Research Institute and Tata Institute
Preprint MRI-PHY/13/93, TIFR/TH/93-6
The Critical Exponents Of The Matrix Valued Gross-Neveu Model
We study the large N limit of the MATRIX valued Gross-Neveu model in 2<d<4
dimensions. The method employed is a combination of the approximate recursion
formula of Polyakov and Wilson with the solution to the zero dimensional large
N counting problem of Makeenko and Zarembo. The model is found to have a phase
transition at a finite value for the critical temperature and the critical
exponents are approximated by nu = 1/(2(d-2)) and eta=d-2. We test the validity
of the approximation by applying it to the usual vector models where it is
found to yield exact results to leading order in 1/N.Comment: 19 pages, LaTeX.2e + macro epsfig. Two eps figures, four LeTeX
picture
Hermitian Matrix Model with Plaquette Interaction
We study a hermitian -matrix model with plaquette interaction,
. By means of a conformal transformation we rewrite the
model as an model on a random lattice with a non polynomial potential.
This allows us to solve the model exactly. We investigate the critical
properties of the plaquette model and find that for the model
belongs to the same universality class as the model on a random lattice.Comment: 15 pages, no figures, two references adde
Topological Field Theory Interpretations and LG Representation of c=1 String Theory
We analyze the topological nature of string theory at the self--dual
radius. We find that it admits two distinct topological field theory structures
characterized by two different puncture operators. We show it first in the
unperturbed theory in which the only parameter is the cosmological constant,
then in the presence of any infinitesimal tachyonic perturbation. We also
discuss in detail a Landau--Ginzburg representation of one of the two
topological field theory structures.Comment: 25 pages, LaTeX, report number adde
Summability of Superstring Theory
Several arguments are given for the summability of the superstring
perturbation series. Whereas the Schottky group coordinatization of moduli
space may be used to provide refined estimates of large-order bosonic string
amplitudes, the super-Schottky group variables define a measure for the
supermoduli space integral which leads to upper bounds on superstring
scattering amplitudes.Comment: 11 pages, TeX. A remark about C-cycles and dividing cycles and two
references have been added to the pape
Extended Toda lattice hierarchy, extended two-matrix model and c=1 string theory
We show how the two--matrix model and Toda lattice hierarchy presented in a
previous paper can be solved exactly: we obtain compact formulas for
correlators of pure tachyonic states at every genus. We then extend the model
to incorporate a set of discrete states organized in finite dimensional
representations. We solve also this extended model and find the correlators of
the discrete states by means of the constraints and the flow equations. Our
results coincide with the ones existing in the literature in those cases in
which particular correlators have been explicitly calculated. We conclude that
the extented two--matrix model is a realization of the discrete states of
string theory.Comment: 34 pages, LaTeX, SISSA 84/94/EP, BONN-HE-08/9
- …