41 research outputs found
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
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
Boundary Flows in general Coset Theories
In this paper we study the boundary effects for off-critical integrable field
theories which have close analogs with integrable lattice models. Our models
are the coset conformal field theories
perturbed by integrable boundary and bulk operators. The boundary interactions
are encoded into the boundary reflection matrix. Using the TBA method, we
verify the flows of the conformal BCs by computing the boundary entropies.
These flows of the BCs have direct interpretations for the fusion RSOS lattice
models. For super CFTs () we show that these flows are possible only for
the Neveu-Schwarz sector and are consistent with the lattice results. The
models we considered cover a wide class of integrable models. In particular, we
show how the the impurity spin is screened by electrons for the -channel
Kondo model by taking limit. We also study the problem using an
independent method based on the boundary roaming TBA. Our numerical results are
consistent with the boundary CFTs and RSOS TBA analysis.Comment: 22 pages, 3 postscript figure file
Bootstrap in Supersymmetric Liouville Field Theory. I. NS Sector
A four point function of basic Neveu-Schwarz exponential fields is
constructed in the N = 1 supersymmetric Liouville field theory. Although the
basic NS structure constants were known previously, we present a new
derivation, based on a singular vector decoupling in the NS sector. This allows
to stay completely inside the NS sector of the space of states, without
referencing to the Ramond fields. The four-point construction involves also the
NS blocks, for which we suggest a new recursion representation, the so-called
elliptic one. The bootstrap conditions for this four point correlation function
are verified numerically for different values of the parameters
On scaling fields in Ising models
We study the space of scaling fields in the symmetric models with the
factorized scattering and propose simplest algebraic relations between form
factors induced by the action of deformed parafermionic currents. The
construction gives a new free field representation for form factors of
perturbed Virasoro algebra primary fields, which are parafermionic algebra
descendants. We find exact vacuum expectation values of physically important
fields and study correlation functions of order and disorder fields in the form
factor and CFT perturbation approaches.Comment: 2 Figures, jetpl.cl
Boundary RG Flow Associated with the AKNS Soliton Hierarchy
We introduce and study an integrable boundary flow possessing an infinite
number of conserving charges which can be thought of as quantum counterparts of
the Ablowitz, Kaup, Newell and Segur Hamiltonians. We propose an exact
expression for overlap amplitudes of the boundary state with all primary states
in terms of solutions of certain ordinary linear differential equation. The
boundary flow is terminated at a nontrivial infrared fixed point. We identify a
form of whole boundary state corresponding to this fixed point.Comment: 54 page
Sigma models as perturbed conformal field theories
We show that two-dimensional sigma models are equivalent to certain perturbed
conformal field theories. When the fields in the sigma model take values in a
space G/H for a group G and a maximal subgroup H, the corresponding conformal
field theory is the limit of the coset model , and the
perturbation is related to the current of G. This correspondence allows us for
example to find the free energy for the "O(n)" (=O(n)/O(n-1)) sigma model at
non-zero temperature. It also results in a new approach to the CP^{n} model.Comment: 4 pages. v2: corrects typos (including several in the published
version
Non-critical string pentagon equations and their solutions
We derive pentagon type relations for the 3-point boundary tachyon
correlation functions in the non-critical open string theory with generic
c_{matter} < 1 and study their solutions in the case of FZZ branes. A new
general formula for the Liouville 3-point factor is derived.Comment: 18 pages, harvmac; misprints corrected, section 3.2 extended, a new
general formula for the Liouville 3-point factor adde