Nonrenormalization Theorem for Gauge Coupling in 2+1D

We prove that \be-function of the gauge coupling in $2+1D$ gauge theory coupled to any renormalizable system of spinor and scalar fields is zero. This result holds both when the gauge field action is the Chern-Simons action and when it is the topologically massive action.Comment: 8 pages, LaTeX file, CALT-68-191

D-branes in Topological Minimal Models: the Landau-Ginzburg Approach

We study D-branes in topologically twisted N=2 minimal models using the Landau-Ginzburg realization. In the cases of A and D-type minimal models we provide what we believe is an exhaustive list of topological branes and compute the corresponding boundary OPE algebras as well as all disk correlators. We also construct examples of topological branes in E-type minimal models. We compare our results with the boundary state formalism, where possible, and find agreement.Comment: 29 pages, late

The Landau-Ginzburg to Calabi-Yau Dictionary for D-Branes

Based on work by Orlov, we give a precise recipe for mapping between B-type D-branes in a Landau-Ginzburg orbifold model (or Gepner model) and the corresponding large-radius Calabi-Yau manifold. The D-branes in Landau-Ginzburg theories correspond to matrix factorizations and the D-branes on the Calabi-Yau manifolds are objects in the derived category. We give several examples including branes on quotient singularities associated to weighted projective spaces. We are able to confirm several conjectures and statements in the literature.Comment: 24 pages, refs added + minor correctio

Boundary states, matrix factorisations and correlation functions for the E-models

The open string spectra of the B-type D-branes of the N=2 E-models are calculated. Using these results we match the boundary states to the matrix factorisations of the corresponding Landau-Ginzburg models. The identification allows us to calculate specific terms in the effective brane superpotential of E_6 using conformal field theory methods, thereby enabling us to test results recently obtained in this context.Comment: 20 pages, no figure

Tensor Product and Permutation Branes on the Torus

We consider B-type D-branes in the Gepner model consisting of two minimal models at k=2. This Gepner model is mirror to a torus theory. We establish the dictionary identifying the B-type D-branes of the Gepner model with A-type Neumann and Dirichlet branes on the torus.Comment: 26 page

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

N=2 Liouville Theory with Boundary

We study N=2 Liouville theory with arbitrary central charge in the presence of boundaries. After reviewing the theory on the sphere and deriving some important structure constants, we investigate the boundary states of the theory from two approaches, one using the modular transformation property of annulus amplitudes and the other using the bootstrap of disc two-point functions containing degenerate bulk operators. The boundary interactions describing the boundary states are also proposed, based on which the precise correspondence between boundary states and boundary interactions is obtained. The open string spectrum between D-branes is studied from the modular bootstrap approach and also from the reflection relation of boundary operators, providing a consistency check for the proposal.Comment: 1+48 pages, no figure. typos corrected and references added. the version to appear in JHE

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

D-branes on general N=1 backgrounds: superpotentials and D-terms

We study the dynamics governing space-time filling D-branes on Type II flux backgrounds preserving four-dimensional N=1 supersymmetry. The four-dimensional superpotentials and D-terms are derived. The analysis is kept on completely general grounds thanks to the use of recently proposed generalized calibrations, which also allow one to show the direct link of the superpotentials and D-terms with BPS domain walls and cosmic strings respectively. In particular, our D-brane setting reproduces the tension of D-term strings found from purely four-dimensional analysis. The holomorphicity of the superpotentials is also studied and a moment map associated to the D-terms is proposed. Among different examples, we discuss an application to the study of D7-branes on SU(3)-structure backgrounds, which reproduces and generalizes some previous results.Comment: 50 pages; v2: table of contents, some clarifications and references added; v3: typos corrected and references adde