64 research outputs found
N=1 SUSY Conformal Block Recursive Relations
We present explicit recursive relations for the four-point superconformal
block functions that are essentially particular contributions of the given
conformal class to the four-point correlation function. The approach is based
on the analytic properties of the superconformal blocks as functions of the
conformal dimensions and the central charge of the superconformal algebra. The
results are compared with the explicit analytic expressions obtained for
special parameter values corresponding to the truncated operator product
expansion. These recursive relations are an efficient tool for numerically
studying the four-point correlation function in Super Conformal Field Theory in
the framework of the bootstrap approach, similar to that in the case of the
purely conformal symmetry.Comment: 12 pages, typos corrected, reference adde
On two-dimensional quantum gravity and quasiclassical integrable hierarchies
The main results for the two-dimensional quantum gravity, conjectured from
the matrix model or integrable approach, are presented in the form to be
compared with the world-sheet or Liouville approach. In spherical limit the
integrable side for minimal string theories is completely formulated using
simple manipulations with two polynomials, based on residue formulas from
quasiclassical hierarchies. Explicit computations for particular models are
performed and certain delicate issues of nontrivial relations among them are
discussed. They concern the connections between different theories, obtained as
expansions of basically the same stringy solution to dispersionless KP
hierarchy in different backgrounds, characterized by nonvanishing background
values of different times, being the simplest known example of change of the
quantum numbers of physical observables, when moving to a different point in
the moduli space of the theory.Comment: 20 pages, based on talk presented at the conference "Liouville field
theory and statistical models", dedicated to the memory of Alexei
Zamolodchikov, Moscow, June 200
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
Higher Equations of Motion in N = 1 SUSY Liouville Field Theory
Similarly to the ordinary bosonic Liouville field theory, in its N=1
supersymmetric version an infinite set of operator valued relations, the
``higher equations of motions'', holds. Equations are in one to one
correspondence with the singular representations of the super Virasoro algebra
and enumerated by a couple of natural numbers . We demonstrate
explicitly these equations in the classical case, where the equations of type
survive and can be interpreted directly as relations for classical
fields. General form of the higher equations of motion is established in the
quantum case, both for the Neveu-Schwarz and Ramond series.Comment: Two references adde
Modular Integrals in Minimal Super Liouville Gravity
The four-point integral of the minimal super Liouville gravity on the sphere
is evaluated numerically. The integration procedure is based on the effective
elliptic parameterization of the moduli space. The analysis is performed for a
few different gravitational four-point amplitudes. The results agree with the
analytic results recently obtained using the Higher super Liouville equations
of motion.Comment: 20 pages, 2 figure
A remark on the three approaches to 2D Quantum gravity
The one-matrix model is considered. The generating function of the
correlation numbers is defined in such a way that this function coincide with
the generating function of the Liouville gravity. Using the Kontsevich theorem
we explain that this generating function is an analytic continuation of the
generating function of the Topological gravity. We check the topological
recursion relations for the correlation functions in the -critical Matrix
model.Comment: 11 pages. Title changed, presentation improve
Higher Equations of Motion in Liouville Field Theory
An infinite set of operator-valued relations in Liouville field theory is
established. These relations are enumerated by a pair of positive integers
, the first representative being the usual Liouville equation of
motion. The relations are proven in the framework of conformal field theory on
the basis of exact structure constants in the Liouville operator product
expansions. Possible applications in 2D gravity are discussed.Comment: Contribution to the proceedings of the VI International Conference
``CFT and Integrable Models'', Chernogolovka, Russia, September 200
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
Integrable Circular Brane Model and Coulomb Charging at Large Conduction
We study a model of 2D QFT with boundary interaction, in which two-component
massless Bose field is constrained to a circle at the boundary. We argue that
this model is integrable at two values of the topological angle,
and . For we propose exact partition function in terms
of solutions of ordinary linear differential equation. The circular brane model
is equivalent to the model of quantum Brownian dynamics commonly used in
describing the Coulomb charging in quantum dots, in the limit of small
dimensionless resistance of the tunneling contact. Our proposal
translates to partition function of this model at integer charge.Comment: 20 pages, minor change
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