Permutation branes and linear matrix factorisations

All the known rational boundary states for Gepner models can be regarded as permutation branes. On general grounds, one expects that topological branes in Gepner models can be encoded as matrix factorisations of the corresponding Landau-Ginzburg potentials. In this paper we identify the matrix factorisations associated to arbitrary B-type permutation branes.Comment: 43 pages. v2: References adde

Triangle-generation in topological D-brane categories

Tachyon condensation in topological Landau-Ginzburg models can generally be studied using methods of commutative algebra and properties of triangulated categories. The efficiency of this approach is demonstrated by explicitly proving that every D-brane system in all minimal models of type ADE can be generated from only one or two fundamental branes.Comment: 34 page

B-type defects in Landau-Ginzburg models

We consider Landau-Ginzburg models with possibly different superpotentials glued together along one-dimensional defect lines. Defects preserving B-type supersymmetry can be represented by matrix factorisations of the difference of the superpotentials. The composition of these defects and their action on B-type boundary conditions is described in this framework. The cases of Landau-Ginzburg models with superpotential W=X^d and W=X^d+Z^2 are analysed in detail, and the results are compared to the CFT treatment of defects in N=2 superconformal minimal models to which these Landau-Ginzburg models flow in the IR.Comment: 50 pages, 2 figure

D-branes in Toroidal Orbifolds and Mirror Symmetry

We study D-branes extended in T^2/Z_4 using the mirror description as a tensor product of minimal models. We describe branes in the mirror both as boundary states in minimal models and as matrix factorizations in the corresponding Landau-Ginzburg model. We isolate a minimal set of branes and give a geometric interpretation of these as D1-branes constrained to the orbifold fixed points. This picture is supported both by spacetime arguments and by the explicit construction of the boundary states, adapting the known results for rational boundary states in the minimal models. Similar techniques apply to a larger class of toroidal orbifolds.Comment: 30 pages, 2 figure

A Synoptic, Multiwavelength Analysis of a Large Quasar Sample

We present variability and multi-wavelength photometric information for the 933 known quasars in the QUEST Variability Survey. These quasars are grouped into variable and non-variable populations based on measured variability confidence levels. In a time-limited synoptic survey, we detect an anti-correlation between redshift and the likelihood of variability. Our comparison of variability likelihood to radio, IR, and X-ray data is consistent with earlier quasar studies. Using already-known quasars as a template, we introduce a light curve morphology algorithm that provides an efficient method for discriminating variable quasars from periodic variable objects in the absence of spectroscopic information. The establishment of statistically robust trends and efficient, non-spectroscopic selection algorithms will aid in quasar identification and categorization in upcoming massive synoptic surveys. Finally, we report on three interesting variable quasars, including variability confirmation of the BL Lac candidate PKS 1222+037.Comment: AJ, accepted for publication 15 Dec 200

Integrability of the N=2 boundary sine-Gordon model

We construct a boundary Lagrangian for the N=2 supersymmetric sine-Gordon model which preserves (B-type) supersymmetry and integrability to all orders in the bulk coupling constant g. The supersymmetry constraint is expressed in terms of matrix factorisations.Comment: LaTeX, 19 pages, no figures; v2: title changed, minor improvements, refs added, to appear in J. Phys. A: Math. Ge

Symmetries of perturbed conformal field theories

The symmetries of perturbed conformal field theories are analysed. We explain which generators of the chiral algebras of a bulk theory survive a perturbation by an exactly marginal bulk field. We also study the behaviour of D-branes under current-current bulk deformations. We find that the branes always continue to preserve as much symmetry as they possibly can, i.e. as much as is preserved in the bulk. We illustrate these findings with several examples, including permutation branes in WZW models and B-type D-branes in Gepner models.Comment: 30 pages, 3 figures. V2: Small error in eq. (2.14) correcte

D-brane superpotentials and RG flows on the quintic

The behaviour of D2-branes on the quintic under complex structure deformations is analysed by combining Landau-Ginzburg techniques with methods from conformal field theory. It is shown that the boundary renormalisation group flow induced by the bulk deformations is realised as a gradient flow of the effective space time superpotential which is calculated explicitly to all orders in the boundary coupling constant.Comment: 24 pages, 1 figure, v2:Typo in (3.14) correcte

Matrix factorisations and D-branes on K3

D-branes on K3 are analysed from three different points of view. For deformations of hypersurfaces in weighted projected space we use geometrical methods as well as matrix factorisation techniques. Furthermore, we study the D-branes on the T^4/\Z_4 orbifold line in conformal field theory. The behaviour of the D-branes under deformations of the bulk theory are studied in detail, and good agreement between the different descriptions is found.Comment: 35 pages, no figure