130 research outputs found
Defect flows in minimal models
In this paper we study a simple example of a two-parameter space of
renormalisation group flows of defects in Virasoro minimal models. We use a
combination of exact results, perturbation theory and the truncated conformal
space approach to search for fixed points and investigate their nature. For the
Ising model, we confirm the recent results of Fendley et al. In the case of
central charge close to one, we find six fixed points, five of which we can
identify in terms of known defects and one of which we conjecture is a new
non-trivial conformal defect. We also include several new results on exact
properties of perturbed defects and on the renormalisation group in the
truncated conformal space approach.Comment: 35 pages, 21 figures. 1 reference adde
Generalised permutation branes
We propose a new class of non-factorising D-branes in the product group GxG
where the fluxes and metrics on the two factors do not necessarily coincide.
They generalise the maximally symmetric permutation branes which are known to
exist when the fluxes agree, but break the symmetry down to the diagonal
current algebra in the generic case. Evidence for the existence of these branes
comes from a Lagrangian description for the open string world-sheet and from
effective Dirac-Born-Infeld theory. We state the geometry, gauge fields and, in
the case of SU(2)xSU(2), tensions and partial results on the open string
spectrum. In the latter case the generalised permutation branes provide a
natural and complete explanation for the charges predicted by K-theory
including their torsion.Comment: 33 pages, 6 figures, v2: Extended discussion of K-theory
interpretation of our branes for products of higher rank groups in the
conclusions; v3: Correction of formula (35) and adjustment of the discussion
below equation (45) (no change of result). Footnote 9 points out a previously
unnoticed subtlety and provides a reference to a more detailed discussio
The abelian cosets of the Heisenberg group
In this paper we study the abelian cosets of the H(4) WZW model. They
coincide or are related to several interesting three-dimensional backgrounds
such as the Melvin model, the conical point-particle space-times and the null
orbifold. We perform a detailed CFT analysis of all the models and compute the
coset characters as well as some typical three-point couplings of coset
primaries.Comment: 26 pages; v2: minor typos corrected, also added section 3.3 and 4.3
with a few comments on a third class of geometries that have not been
discussed in v
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
adde
D-brane charges on SO(3)
In this letter we discuss charges of D-branes on the group manifold SO(3).
Our discussion will be based on a conformal field theory analysis of boundary
states in a Z_2-orbifold of SU(2). This orbifold differs from the one recently
discussed by Gaberdiel and Gannon in its action on the fermions and leads to a
drastically different charge group. We shall consider maximally symmetric
branes as well as branes with less symmetry, and find perfect agreement with a
recent computation of the corresponding K-theory groups.Comment: 11 pages, 1 figure. Some comments adde
The diagonal cosets of the Heisenberg group
In this paper we study the diagonal cosets of the non-compact H4 WZW model.
Generalising earlier work by Antoniadis and Obers, we provide an exact
world-sheet description for several families of non-maximally symmetric
gravitational plane waves with background NS fluxes. We show that the
sigma-models that correspond to an asymmetric action of the gauge group
smoothly interpolate between singular and non-singular plane waves. We also
analyse the representations of the coset chiral algebra and derive the spectrum
of all the models.Comment: 42 pages, v2: more explicit expressions for the background fields in
section 3.2.2, reference [49] added, some typos correcte
On D-branes in the Nappi-Witten and GMM gauged WZW models
We construct D-branes in the Nappi-Witten (NW) and
Guadagnini-Martellini-Mintchev (GMM) gauged WZW models. For the NW and GMM models we present
the explicit equations describing the D-brane hypersurfaces in their target
spaces. In the latter case we show that the D-branes are classified according
to the Cardy theorem. We also present the semiclassical mass computation and
find its agreement with the CFT predictions.Comment: 16 pages, harvma
Branching rules of semi-simple Lie algebras using affine extensions
We present a closed formula for the branching coefficients of an embedding p
in g of two finite-dimensional semi-simple Lie algebras. The formula is based
on the untwisted affine extension of p. It leads to an alternative proof of a
simple algorithm for the computation of branching rules which is an analog of
the Racah-Speiser algorithm for tensor products. We present some simple
applications and describe how integral representations for branching
coefficients can be obtained. In the last part we comment on the relation of
our approach to the theory of NIM-reps of the fusion rings of WZW models with
chiral algebra g_k. In fact, it turns out that for these models each embedding
p in g induces a NIM-rep at level k to infinity. In cases where these NIM-reps
can be be extended to finite level, we obtain a Verlinde-like formula for
branching coefficients.Comment: 11 pages, LaTeX, v2: one reference added, v3: Clarified proof of
Theorem 2, completely rewrote and extended Section 5 (relation to CFT), added
various references. Accepted for publication in J. Phys.
Quantization of Wilson loops in Wess-Zumino-Witten models
We describe a non-perturbative quantization of classical Wilson loops in the
WZW model. The quantized Wilson loop is an operator acting on the Hilbert space
of closed strings and commuting either with the full Kac-Moody chiral algebra
or with one of its subalgebras. We prove that under open/closed string duality,
it is dual to a boundary perturbation of the open string theory. As an
application, we show that such operators are useful tools for identifying fixed
points of the boundary renormalization group flow.Comment: 24 pages. Version published in JHE
The charges of a twisted brane
The charges of the twisted D-branes of certain WZW models are determined. The
twisted D-branes are labelled by twisted representations of the affine algebra,
and their charge is simply the ground state multiplicity of the twisted
representation. It is shown that the resulting charge group is isomorphic to
the charge group of the untwisted branes, as had been anticipated from a
K-theory calculation. Our arguments rely on a number of non-trivial Lie
theoretic identities.Comment: 27 pages, 1 figure, harvmac (b
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