549 research outputs found
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
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
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
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
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
Opening Mirror Symmetry on the Quintic
Aided by mirror symmetry, we determine the number of holomorphic disks ending
on the real Lagrangian in the quintic threefold. The tension of the domainwall
between the two vacua on the brane, which is the generating function for the
open Gromov-Witten invariants, satisfies a certain extension of the
Picard-Fuchs differential equation governing periods of the mirror quintic. We
verify consistency of the monodromies under analytic continuation of the
superpotential over the entire moduli space. We reproduce the first few
instanton numbers by a localization computation directly in the A-model, and
check Ooguri-Vafa integrality. This is the first exact result on open string
mirror symmetry for a compact Calabi-Yau manifold.Comment: 26 pages. v2: minor corrections and improvement
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
Moduli Webs and Superpotentials for Five-Branes
We investigate the one-parameter Calabi-Yau models and identify families of
D5-branes which are associated to lines embedded in these manifolds. The moduli
spaces are given by sets of Riemann curves, which form a web whose intersection
points are described by permutation branes. We arrive at a geometric
interpretation for bulk-boundary correlators as holomorphic differentials on
the moduli space and use this to compute effective open-closed superpotentials
to all orders in the open string couplings. The fixed points of D5-brane moduli
under bulk deformations are determined.Comment: 41 pages, 1 figur
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