342 research outputs found
Bosonic Field Propagators on Algebraic Curves
In this paper we investigate massless scalar field theory on non-degenerate
algebraic curves. The propagator is written in terms of the parameters
appearing in the polynomial defining the curve. This provides an alternative to
the language of theta functions. The main result is a derivation of the third
kind differential normalized in such a way that its periods around the homology
cycles are purely imaginary. All the physical correlation functions of the
scalar fields can be expressed in terms of this object. This paper contains a
detailed analysis of the techniques necessary to study field theories on
algebraic curves. A simple expression of the scalar field propagator is found
in a particular case in which the algebraic curves have internal symmetry
and one of the fields is located at a branch point.Comment: 26 pages, TeX + harvma
Blocking of Dynamical Triangulations with Matter
We use the recently proposed node decimation algorithm for blocking dynamical
geometries to investigate a class of models, with central charge greater than
unity, coupled to 2D gravity. We demonstrate that the blocking preserves the
fractal structure of the surfaces.Comment: Talk presented at LATTICE96(gravity), 3 pages, LaTeX, espcrc2.st
On the mass spectrum of the two-dimensional O(3) sigma model with theta term
Form Factor Perturbation Theory is applied to study the spectrum of the O(3)
non--linear sigma model with the topological term in the vicinity of . Its effective action near this value is given by the non--integrable
double Sine--Gordon model. Using previous results by Affleck and the explicit
expressions of the Form Factors of the exponential operators , we show that the spectrum consists of a stable triplet
of massive particles for all values of and a singlet state of higher
mass. The singlet is a stable particle only in an interval of values of
close to whereas it becomes a resonance below a critical value
.Comment: 4 pages REVTEX4, 2 figures reference added,corrected typo
Spin-spin correlation functions of spin systems coupled to 2-d quantum gravity for
We perform Monte Carlo simulations of 2-d dynamically triangulated surfaces
coupled to Ising and three--states Potts model matter. By measuring spin-spin
correlation functions as a function of the geodesic distance we provide
substantial evidence for a diverging correlation length at . The
corresponding scaling exponents are directly related to the KPZ exponents of
the matter fields as conjectured in [4] (NPB454(1995)313).Comment: Talk presented at LATTICE96(gravity
Renormalization of the Topological Charge in Yang-Mills Theory
The conditions leading to a nontrivial renormalization of the topological
charge in four--dimensional Yang--Mills theory are discussed. It is shown that
if the topological term is regarded as the limit of a certain nontopological
interaction, quantum effects due to the gauge bosons lead to a finite
multiplicative renormalization of the theta--parameter while fermions give rise
to an additional shift of theta. A truncated form of an exact renormalization
group equation is used to study the scale dependence of the theta--parameter.
Possible implications for the strong CP--problem of QCD are discussed.Comment: 31 pages, late
Multivalued Fields on the Complex Plane and Conformal Field Theories
In this paper a class of conformal field theories with nonabelian and
discrete group of symmetry is investigated. These theories are realized in
terms of free scalar fields starting from the simple systems and scalar
fields on algebraic curves. The Knizhnik-Zamolodchikov equations for the
conformal blocks can be explicitly solved. Besides of the fact that one obtains
in this way an entire class of theories in which the operators obey a
nonstandard statistics, these systems are interesting in exploring the
connection between statistics and curved space-times, at least in the two
dimensional case.Comment: (revised version), 30 pages + one figure (not included), (requires
harvmac.tex), LMU-TPW 92-1
Geometric Transformations and NCCS Theory in the Lowest Landau Level
Chern-Simons type gauge field is generated by the means of the singular area
preserving transformations in the lowest Landau level of electrons forming
fractional quantum Hall state. Dynamics is governed by the system of
constraints which correspond to the Gauss law in the non-commutative
Chern-Simons gauge theory and to the lowest Landau level condition in the
picture of composite fermions. Physically reasonable solution to this
constraints corresponds to the Laughlin state. It is argued that the model
leads to the non-commutative Chern-Simons theory of the QHE and composite
fermions.Comment: Latex, 13 page
Critical Exponents near a Random Fractal Boundary
The critical behaviour of correlation functions near a boundary is modified
from that in the bulk. When the boundary is smooth this is known to be
characterised by the surface scaling dimension \xt. We consider the case when
the boundary is a random fractal, specifically a self-avoiding walk or the
frontier of a Brownian walk, in two dimensions, and show that the boundary
scaling behaviour of the correlation function is characterised by a set of
multifractal boundary exponents, given exactly by conformal invariance
arguments to be \lambda_n = 1/48 (\sqrt{1+24n\xt}+11)(\sqrt{1+24n\xt}-1).
This result may be interpreted in terms of a scale-dependent distribution of
opening angles of the fractal boundary: on short distance scales these
are sharply peaked around . Similar arguments give the
multifractal exponents for the case of coupling to a quenched random bulk
geometry.Comment: 13 pages. Comments on relation to results in quenched random bulk
added, and on relation to other recent work. Typos correcte
correction to free energy in hermitian two-matrix model
Using the loop equations we find an explicit expression for genus 1
correction in hermitian two-matrix model in terms of holomorphic objects
associated to spectral curve arising in large N limit. Our result generalises
known expression for in hermitian one-matrix model. We discuss the
relationship between , Bergmann tau-function on Hurwitz spaces, G-function
of Frobenius manifolds and determinant of Laplacian over spectral curve
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