1,121 research outputs found
Structure Constants and Conformal Bootstrap in Liouville Field Theory
An analytic expression is proposed for the three-point function of the
exponential fields in the Liouville field theory on a sphere. In the classical
limit it coincides with what the classical Liouville theory predicts. Using
this function as the structure constant of the operator algebra we construct
the four-point function of the exponential fields and verify numerically that
it satisfies the conformal bootstrap equations, i.e., that the operator algebra
thus defined is associative. We consider also the Liouville reflection
amplitude which follows explicitly from the structure constants.Comment: 31 pages, 2 Postscript figures. Important note about existing (but
unfortunately previously unknown to us) paper which has significant overlap
with this work is adde
Conserved charges in the chiral 3-state Potts model
We consider the perturbations of the 3-state Potts conformal field theory
introduced by Cardy as a description of the chiral 3-state Potts model. By
generalising Zamolodchikov's counting argument and by explicit calculation we
find new inhomogeneous conserved currents for this theory. We conjecture the
existence of an infinite set of conserved currents of this form and discuss
their relevance to the description of the chiral Potts models
Critical interfaces and duality in the Ashkin Teller model
We report on the numerical measures on different spin interfaces and FK
cluster boundaries in the Askhin-Teller (AT) model. For a general point on the
AT critical line, we find that the fractal dimension of a generic spin cluster
interface can take one of four different possible values. In particular we
found spin interfaces whose fractal dimension is d_f=3/2 all along the critical
line. Further, the fractal dimension of the boundaries of FK clusters were
found to satisfy all along the AT critical line a duality relation with the
fractal dimension of their outer boundaries. This result provides a clear
numerical evidence that such duality, which is well known in the case of the
O(n) model, exists in a extended CFT.Comment: 5 pages, 4 figure
Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks
Liouville field theory on a sphere is considered. We explicitly derive a
differential equation for four-point correlation functions with one degenerate
field . We introduce and study also a class of four-point
conformal blocks which can be calculated exactly and represented by finite
dimensional integrals of elliptic theta-functions for arbitrary intermediate
dimension. We study also the bootstrap equations for these conformal blocks and
derive integral representations for corresponding four-point correlation
functions. A relation between the one-point correlation function of a primary
field on a torus and a special four-point correlation function on a sphere is
proposed
g-function in perturbation theory
We present some explicit computations checking a particular form of gradient
formula for a boundary beta function in two-dimensional quantum field theory on
a disc. The form of the potential function and metric that we consider were
introduced in hep-th/9210065, hep-th/9311177 in the context of background
independent open string field theory. We check the gradient formula to the
third order in perturbation theory around a fixed point. Special consideration
is given to situations when resonant terms are present exhibiting logarithmic
divergences and universal nonlinearities in beta functions. The gradient
formula is found to work to the given order.Comment: 1+14 pages, Latex; v.2: typos corrected; v.3: minor corrections, to
appear in IJM
Form Factors in Off--Critical Superconformal Models
We discuss the determination of the lowest Form Factors relative to the trace
operators of N=1 Super Sinh-Gordon Model. Analytic continuations of these Form
Factors as functions of the coupling constant allows us to study a series of
models in a uniform way, among these the latest model of the Roaming Series and
a class of minimal supersymmetric models.Comment: 11 pages, 2 Postscript figures. To appear in the Proceedings of the
Euroconference on New Symmetries in Statistical Mech. and Cond. Mat. Physics,
Torino, July 20- August 1 199
On the Finite Temperature Formalism in Integrable Quantum Field Theories
Two different theoretical formulations of the finite temperature effects have
been recently proposed for integrable field theories. In order to decide which
of them is the correct one, we perform for a particular model an explicit check
of their predictions for the one-point function of the trace of the
stress-energy tensor, a quantity which can be independently determined by the
Thermodynamical Bethe Ansatz.Comment: 12 pages, corrected some typos and an equatio
- …