245 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
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
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
On third Poisson structure of KdV equation
The third Poisson structure of KdV equation in terms of canonical ``free
fields'' and reduced WZNW model is discussed. We prove that it is
``diagonalized'' in the Lagrange variables which were used before in
formulation of 2D gravity. We propose a quantum path integral for KdV equation
based on this representation.Comment: 6pp, Latex. to appear in ``Proceedings of V conference on
Mathematical Physics, String Theory and Quantum Gravity, Alushta, June 1994''
Teor.Mat.Fiz. 199
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
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
Reconstruction of Zigzag Graphene Edges: Energetics, Kinetics and Residual Defects
Ab initio calculations are performed to study consecutive reconstruction of a
zigzag graphene edge. According to the obtained energy profile along the
reaction pathway, the first reconstruction step, formation of the first
pentagon-heptagon pair, is the slowest one, while the growth of an already
nucleated reconstructed edge domain should occur steadily at a much higher
rate. Domains merge into one only in 1/4 of cases when they get in contact,
while in the rest of the cases, residual defects are left. Structure, energy
and magnetic properties of these defects are studied. It is found that
spontaneous formation of pairs of residual defects (i.e. spontaneous domain
nucleation) in the fully reconstructed edge is unlikely at temperatures below
1000 K. Using a kinetic model, we show that the average domain length is of
several m at room temperature and it decreases exponentially upon
increasing the temperature at which the reconstruction takes place.Comment: 5 pages, 4 figure
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
The Block Spin Renormalization Group Approach and Two-Dimensional Quantum Gravity
A block spin renormalization group approach is proposed for the dynamical
triangulation formulation of two-dimensional quantum gravity. The idea is to
update link flips on the block lattice in response to link flips on the
original lattice. Just as the connectivity of the original lattice is meant to
be a lattice representation of the metric, the block links are determined in
such a way that the connectivity of the block lattice represents a block
metric. As an illustration, this approach is applied to the Ising model coupled
to two-dimensional quantum gravity. The correct critical coupling is
reproduced, but the critical exponent is obscured by unusually large finite
size effects.Comment: 10 page
- …