An algorithm for twisted fusion rules

We present an algorithm for an efficient calculation of the fusion rules of twisted representations of untwisted affine Lie algebras. These fusion rules appear in WZW orbifold theories and as annulus coefficients in boundary WZW theories; they provide NIM-reps of the WZW fusion rules.Comment: 8 page

On the hierarchy of symmetry breaking D-branes in group manifolds

We construct the boundary WZNW functional for symmetry breaking D-branes on a group manifold which are localized along a product of a number of twisted conjugacy classes and which preserve an action of an arbitrary continuous subgroup. These branes provide a geometric interpretation for the algebraic formulation of constructing D-branes developed recently in hep-th/0203161. We apply our results to obtain new symmetry breaking and non-factorizing D-branes in the background SL(2,R) x SU(2)

Reflection and Transmission for Conformal Defects

We consider conformal defects joining two conformal field theories along a line. We define two new quantities associated to such defects in terms of expectation values of the stress tensors and we propose them as measures of the reflectivity and transmissivity of the defect. Their properties are investigated and they are computed in a number of examples. We obtain a complete answer for all defects in the Ising model and between certain pairs of minimal models. In the case of two conformal field theories with an enhanced symmetry we restrict ourselves to non-trivial defects that can be obtained by a coset construction.Comment: 32 pages + 13 pages appendix, 12 figures; v2: added eqns (2.7), (2.8) and refs [6,7,39,40], version published in JHE

Asymmetrically gauged WZNW models

Many interesting exactly solvable backgrounds can be obtained by gauging WZNW models asymmetrically. These include the base of the conifold and the time dependent Nappi-Witten background in which a 3-dimensional universe passes through a series of big-bang big-crunch singularities. In this short note we review recent results on the conformal field theory description of asymmetric cosets. In particular, we present formulas for their bulk modular invariant partition functions and for a large number of D-brane boundary states

From Defects to Boundaries

In this paper we describe how relativistic field theories containing defects are equivalent to a class of boundary field theories. As a consequence previously derived results for boundaries can be directly applied to defects, these results include reduction formulas, the Coleman-Thun mechanism and Cutcosky rules. For integrable theories the defect crossing unitarity equation can be derived and defect operator found. For a generic purely transmitting impurity we use the boundary bootstrap method to obtain solutions of the defect Yang-Baxter equation. The groundstate energy on the strip with defects is also calculated.Comment: 14 pages, 10 figures. V2 Removed comparison to RT algebras and added paragraph on the usefulness of transmitting defects in the study of boundary systems. References added. V3 Extended to include application to defect TB

On reduced models for superstrings on AdS_n x S^n

We review the Pohlmeyer reduction procedure of the superstring sigma model on AdS_n x S^n leading to a gauged WZW model with an integrable potential coupled to 2d fermions. In particular, we consider the case of the Green-Schwarz superstring on AdS_3 x S^3 supported by RR flux. The bosonic part of the reduced model is given by the sum of the complex sine-Gordon Lagrangian and its sinh-Gordon counterpart. We determine the corresponding fermionic part and discuss possible existence of hidden 2d supersymmetry in the reduced action. We also elaborate on some general aspects of the Pohlmeyer reduction applied to the AdS_5 x S^5 superstring.Comment: 24 page

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

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

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.

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