15 research outputs found
Topological defects for the free boson CFT
Two different conformal field theories can be joined together along a defect
line. We study such defects for the case where the conformal field theories on
either side are single free bosons compactified on a circle. We concentrate on
topological defects for which the left- and right-moving Virasoro algebras are
separately preserved, but not necessarily any additional symmetries. For the
case where both radii are rational multiples of the self-dual radius we
classify these topological defects. We also show that the isomorphism between
two T-dual free boson conformal field theories can be described by the action
of a topological defect, and hence that T-duality can be understood as a
special type of order-disorder duality.Comment: 43 pages, 4 figure
Geometric construction of D-branes in WZW models
The geometric description of D-branes in WZW models is pushed forward. Our
starting point is a gluing condition\, that matches the model's
chiral currents at the worldsheet boundary through a linear map acting on
the WZW Lie algebra. The equivalence of boundary and gluing conditions of this
type is studied in detail. The analysis involves a thorough discussion of
Frobenius integrability, shows that must be an isometry, and applies to
both metrically degenerate and nondegenerate D-branes. The isometry need
not be a Lie algebra automorphism nor constantly defined over the brane. This
approach, when applied to isometries of the form with a constant Lie
algebra automorphism, validates metrically degenerate -twined conjugacy
classes as D-branes. It also shows that no D-branes exist in semisimple WZW
models for constant\, .Comment: 23 pages, discussion of limitations of the gluing condition approach
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Fermionic Coset, Critical Level W^(2)_4-Algebra and Higher Spins
The fermionic coset is a limit of the pure spinor formulation of the AdS5xS5
sigma model as well as a limit of a nonlinear topological A-model, introduced
by Berkovits. We study the latter, especially its symmetries, and map them to
higher spin algebras.
We show the following. The linear A-model possesses affine
\AKMSA{pgl}{4}{4}_0 symmetry at critical level and its \AKMSA{psl}{4}{4}_0
current-current perturbation is the nonlinear model. We find that the
perturbation preserves -algebra symmetry at critical
level. There is a topological algebra associated to \AKMSA{pgl}{4}{4}_0 with
the properties that the perturbation is BRST-exact. Further, the
BRST-cohomology contains world-sheet supersymmetric symplectic fermions and the
non-trivial generators of the -algebra. The Zhu functor
maps the linear model to a higher spin theory. We analyze its
\SLSA{psl}{4}{4} action and find finite dimensional short multiplets.Comment: 25 page
Massless particles on supergroups and AdS3 x S3 supergravity
Firstly, we study the state space of a massless particle on a supergroup with
a reparameterization invariant action. After gauge fixing the
reparameterization invariance, we compute the physical state space through the
BRST cohomology and show that the quadratic Casimir Hamiltonian becomes
diagonalizable in cohomology. We illustrate the general mechanism in detail in
the example of a supergroup target GL(1|1). The space of physical states
remains an indecomposable infinite dimensional representation of the space-time
supersymmetry algebra. Secondly, we show how the full string BRST cohomology in
the particle limit of string theory on AdS3 x S3 renders the quadratic Casimir
diagonalizable, and reduces the Hilbert space to finite dimensional
representations of the space-time supersymmetry algebra (after analytic
continuation). Our analysis provides an efficient way to calculate the
Kaluza-Klein spectrum for supergravity on AdS3 x S3. It may also be a step
towards the identification of an interesting and simpler subsector of
logarithmic supergroup conformal field theories, relevant to string theory.Comment: 16 pages, 10 figure
Boundary Spectra in Superspace Sigma-Models.
In this note we compute exact boundary spectra for D-instantons in
sigma-models on the supergroup PSL(2|2). Our results are obtained through an
explicit summation of the perturbative expansion for conformal dimensions to
all orders in the curvature radius. The analysis exploits several remarkable
properties of the perturbation series that arises from rescalings of the metric
on PSL(2|2) relative to a fixed Wess-Zumino term. According to Berkovits, Vafa
and Witten, the models are relevant in the context of string theory on AdS3
with non-vanishing RR-flux. The note concludes with a number of comments on
various possible generalizations to other supergroups and higher dimensional
supercoset theories.Comment: 32 pages, 1 figur
New Boundary Conditions for the c=-2 Ghost System.
We investigate a novel boundary condition for the bc system with central
charge c=-2. Its boundary state is constructed and tested in detail. It appears
to give rise to the first example of a local logarithmic boundary sector within
a bulk theory whose Virasoro zero modes are diagonalizable
Branes in the GL(1|1) WZNW-model
We initiate a systematic study of boundary conditions in conformal field
theories with target space supersymmetry. The WZNW model on GL(1|1) is used as
a prototypical example for which we find the complete set of maximally
symmetric branes. This includes a unique brane of maximal super-dimension 2|2,
a 2-parameter family of branes with super-dimension 0|2 and an infinite set of
fully localized branes possessing a single modulus. Members of the latter
family can only exist along certain lines on the bosonic base, much like
fractional branes at orbifold singularities. Our results establish that all
essential algebraic features of Cardy-type boundary theories carry over to the
non-rational logarithmic WZNW model on GL(1|1).Comment: 38 page
From world-sheet supersymmetry to super target spaces
We investigate the relation between N=(2,2) superconformal Lie group WZNW
models and Lie supergroup WZNW models. The B-twist of an exactly marginal
perturbation of the world-sheet superconformal sigma model is the supergroup
model. Moreover, the superconformal currents are expressed in terms of Lie
superalgebra currents in the twisted theory. As applications, we find protected
sectors and boundary actions in the supergroup sigma model. A special example
is the relation between string theory on AdS_3 x S^3 x T^4 in the RNS formalism
and the U(1,1|2) x U(1|1) x U(1|1) supergroup WZNW model.Comment: 37 page
The Sigma Model on Complex Projective Superspaces
The sigma model on projective superspaces CP^{S-1|S} gives rise to a continuous family of interacting 2D conformal field theories which are parametrized by the curvature radius R and the theta angle theta. Our main goal is to determine the spectrum of the model, non-perturbatively as a function of both parameters. We succeed to do so for all open boundary conditions preserving the full global symmetry of the model. In string theory parlor, these correspond to volume filling branes that are equipped with a monopole line bundle and connection. The paper consists of two parts. In the first part, we approach the problem within the continuum formulation. Combining combinatorial arguments with perturbative studies and some simple free field calculations, we determine a closed formula for the partition function of the theory. This is then tested numerically in the second part. There we extend the proposal of [arXiv:0908.1081] for a spin chain regularization of the CP^{S-1|S} model with open boundary conditions and use it to determine the spectrum at the conformal fixed point. The numerical results are in remarkable agreement with the continuum analysis