41 research outputs found
Comments on fusion matrix in N=1 super Liouville field theory
We study several aspects of the super Liouville theory. We show that
certain elements of the fusion matrix in the Neveu-Schwarz sector related to
the structure constants according to the same rules which we observe in
rational conformal field theory. We collect some evidences that these relations
should hold also in the Ramond sector. Using them the Cardy-Lewellen equation
for defects is studied, and defects are constructed.Comment: 28 pages, comment and reference adde
Defects, Non-abelian T-duality, and the Fourier-Mukai transform of the Ramond-Ramond fields
We construct topological defects generating non-abelian T-duality for
isometry groups acting without isotropy. We find that these defects are given
by line bundles on the correspondence space with curvature which can be
considered as a non-abelian generalization of the curvature of the Poincar\`{e}
bundle. We show that the defect equations of motion encode the non-abelian
T-duality transformation. The Fourier-Mukai transform of the Ramond-Ramond
fields generated by the gauge invariant flux of these defects is studied. We
show that it provides elegant and compact way of computation of the
transformation of the Ramond-Ramond fields under the non-abelian T-duality.Comment: 18 pages, minor typos corrected, references adde
On mini-superspace limit of boundary three-point function in Liouville field theory
We study mini-superspace semiclassical limit of the boundary three-point
function in the Liouville field theory. We compute also matrix elements for the
Morse potential quantum mechanics. An exact agreement between the former and
the latter is found. We show that both of them are given by the generalized
hypergeometric functions.Comment: 18 page
On classical and semiclassical properties of the Liouville theory with defects
The Lagrangian of the Liouville theory with topological defects is analyzed
in detail and general solution of the corresponding defect equations of motion
is found. We study the heavy and light semiclassical limits of the defect
two-point function found before via the bootstrap program. We show that the
heavy asymptotic limit is given by the exponential of the Liouville action with
defects, evaluated on the solutions with two singular points. We demonstrate
that the light asymptotic limit is given by the finite dimensional path
integral over solutions of the defect equations of motion with a vanishing
energy-momentum tensor.Comment: 50 pages, typos corrected, references added, comments and
explanations adde
Topological defects in the Liouville field theories with different cosmological constants
We construct topological defects in the Liouville field theory producing jump
in the value of cosmological constant. We construct them using the
Cardy-Lewellen equation for the two-point function with defect. We show that
there are continuous and discrete families of such kind of defects. For the
continuous family of defects we also find the Lagrangian description and check
its agreement with the solution of the Cardy-Lewellen equation using the heavy
asymptotic semiclasscial limit.Comment: 15 page
From rarefied elliptic beta integral to parafermionic star-triangle relation
We consider the rarefied elliptic beta integral in various limiting forms. In
particular, we obtain an integral identity for parafermionic hyperbolic gamma
functions which describes the star-triangle relation for parafermionic
Liouville theory.Comment: 19 page
On Least Action D-Branes
We discuss the effect of relevant boundary terms on the nature of branes.
This is done for toroidal and orbifold compactifications of the bosonic string.
Using the relative minimalization of the boundary entropy as a guiding
principle, we uncover the more stable boundary conditions at different regions
of moduli space. In some cases, Neumann boundary conditions dominate for small
radii while Dirichlet boundary conditions dominate for large radii. The c=1 and
c=2 moduli spaces are studied in some detail. The antisymmetric background
field B is found to have a more limited role in the case of Dirichlet boundary
conditions. This is due to some topological considerations. The results are
subjected to T-duality tests and the special role of the points in moduli space
fixed under T-duality is explained from least-action considerations.Comment: Latex, 20 pages, 2 figures, references adde
S-move matrix in the NS sector of super Liouville field theory
In this paper we calculate matrix of modular transformations of the one-point
toric conformal blocks in the Neveu-Schwarz sector of super Liouville
field theory. For this purpose we use explicit expression for this matrix as
integral of product of certain elements of fusion matrix. This integral is
computed using the chain of integral identities for supersymmetric hyperbolic
gamma functions derived by the degeneration of the integrals of parafermionic
elliptic gamma functions.Comment: 25 page
On canonical quantization of the gauged WZW model with permutation branes
In this paper we perform canonical quantization of the product of the gauged
WZW models on a strip with boundary conditions specified by permutation branes.
We show that the phase space of the -fold product of the gauged WZW model
on a strip with boundary conditions given by permutation branes is
symplectomorphic to the phase space of the double Chern-Simons theory on a
sphere with holes times the time-line with and gauge fields both
coupled to two Wilson lines. For the special case of the topological coset
we arrive at the conclusion that the phase space of the -fold product
of the topological coset on a strip with boundary conditions given by
permutation branes is symplectomorphic to the phase space of Chern-Simons
theory on a Riemann surface of the genus times the time-line with four
Wilson lines.Comment: 18 page