59 research outputs found
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
Toric Calabi-Yau supermanifolds and mirror symmetry
We study mirror symmetry of supermanifolds constructed as fermionic
extensions of compact toric varieties. We mainly discuss the case where the
linear sigma A-model contains as many fermionic fields as there are U(1)
factors in the gauge group. In the mirror super-Landau-Ginzburg B-model, focus
is on the bosonic structure obtained after integrating out all the fermions.
Our key observation is that there is a relation between the super-Calabi-Yau
conditions of the A-model and quasi-homogeneity of the B-model, and that the
degree of the associated superpotential in the B-model is given in terms of the
determinant of the fermion charge matrix of the A-model.Comment: 20 pages, v2: references adde
On Local Calabi-Yau Supermanifolds and Their Mirrors
We use local mirror symmetry to study a class of local Calabi-Yau
super-manifolds with bosonic sub-variety V_b having a vanishing first Chern
class. Solving the usual super- CY condition, requiring the equality of the
total U(1) gauge charges of bosons \Phi_{b} and the ghost like fields \Psi_{f}
one \sum_{b}q_{b}=\sum_{f}Q_{f}, as \sum_{b}q_{b}=0 and \sum_{f}Q_{f}=0,
several examples are studied and explicit results are given for local A_{r}
super-geometries. A comment on purely fermionic super-CY manifolds
corresponding to the special case where q_{b}=0, \forall b and \sum_{f}Q_{f}=0
is also made.\bigskipComment: 17 page
A Note on Computations of D-brane Superpotential
We develop some computational methods for the integrals over the 3-chains on
the compact Calabi-Yau 3-folds that plays a prominent role in the analysis of
the topological B-model in the context of the open mirror symmetry. We discuss
such 3-chain integrals in two approaches. In the first approach, we provide a
systematic algorithm to obtain the inhomogeneous Picard-Fuchs equations. In the
second approach, we discuss the analytic continuation of the period integral to
compute the 3-chain integral directly. The latter direct integration method is
applicable for both on-shell and off-shell formalisms.Comment: 61 pages, 5 figures; v2: typos corrected, minor changes, references
adde
NC Calabi-Yau Orbifolds in Toric Varieties with Discrete Torsion
Using the algebraic geometric approach of Berenstein et {\it al}
(hep-th/005087 and hep-th/009209) and methods of toric geometry, we study non
commutative (NC) orbifolds of Calabi-Yau hypersurfaces in toric varieties with
discrete torsion. We first develop a new way of getting complex mirror
Calabi-Yau hypersurfaces in toric manifolds with a action and analyze the general group of the
discrete isometries of . Then we build a general class of
complex dimension NC mirror Calabi-Yau orbifolds where the non
commutativity parameters are solved in terms of discrete
torsion and toric geometry data of in which the original
Calabi-Yau hypersurfaces is embedded. Next we work out a generalization of the
NC algebra for generic dimensions NC Calabi-Yau manifolds and give various
representations depending on different choices of the Calabi-Yau toric geometry
data. We also study fractional D-branes at orbifold points. We refine and
extend the result for NC to higher dimensional torii orbifolds
in terms of Clifford algebra.Comment: 38 pages, Late
Khovanov-Rozansky Homology and Topological Strings
We conjecture a relation between the sl(N) knot homology, recently introduced
by Khovanov and Rozansky, and the spectrum of BPS states captured by open
topological strings. This conjecture leads to new regularities among the sl(N)
knot homology groups and suggests that they can be interpreted directly in
topological string theory. We use this approach in various examples to predict
the sl(N) knot homology groups for all values of N. We verify that our
predictions pass some non-trivial checks.Comment: 25 pages, 2 figures, harvmac; minor corrections, references adde
Comments on D-branes in Kazama-Suzuki models and Landau-Ginzburg theories
We study D-branes in Kazama-Suzuki models by means of the boundary state
description. We can identify the boundary states of Kazama-Suzuki models with
the solitons in N=2 Landau-Ginzburg theories. We also propose a geometrical
interpretation of the boundary states in Kazama-Suzuki models.Comment: 28 pages, 2 figure
Rigidity and defect actions in Landau-Ginzburg models
Studying two-dimensional field theories in the presence of defect lines
naturally gives rise to monoidal categories: their objects are the different
(topological) defect conditions, their morphisms are junction fields, and their
tensor product describes the fusion of defects. These categories should be
equipped with a duality operation corresponding to reversing the orientation of
the defect line, providing a rigid and pivotal structure. We make this
structure explicit in topological Landau-Ginzburg models with potential x^d,
where defects are described by matrix factorisations of x^d-y^d. The duality
allows to compute an action of defects on bulk fields, which we compare to the
corresponding N=2 conformal field theories. We find that the two actions differ
by phases.Comment: 53 pages; v2: clarified exposition of pivotal structures, corrected
proof of theorem 2.13, added remark 3.9; version to appear in CM
Non-birational twisted derived equivalences in abelian GLSMs
In this paper we discuss some examples of abelian gauged linear sigma models
realizing twisted derived equivalences between non-birational spaces, and
realizing geometries in novel fashions. Examples of gauged linear sigma models
with non-birational Kahler phases are a relatively new phenomenon. Most of our
examples involve gauged linear sigma models for complete intersections of
quadric hypersurfaces, though we also discuss some more general cases and their
interpretation. We also propose a more general understanding of the
relationship between Kahler phases of gauged linear sigma models, namely that
they are related by (and realize) Kuznetsov's `homological projective duality.'
Along the way, we shall see how `noncommutative spaces' (in Kontsevich's sense)
are realized physically in gauged linear sigma models, providing examples of
new types of conformal field theories. Throughout, the physical realization of
stacks plays a key role in interpreting physical structures appearing in GLSMs,
and we find that stacks are implicitly much more common in GLSMs than
previously realized.Comment: 54 pages, LaTeX; v2: typo fixe
Defects and Bulk Perturbations of Boundary Landau-Ginzburg Orbifolds
We propose defect lines as a useful tool to study bulk perturbations of
conformal field theories, in particular to analyse the induced renormalisation
group flows of boundary conditions. As a concrete example we investigate bulk
perturbations of N=2 supersymmetric minimal models. To these perturbations we
associate a special class of defects between the respective UV and IR theories,
whose fusion with boundary conditions indeed reproduces the behaviour of the
latter under the corresponding RG flows. v2: Some explanations added in section
4, minor changes.Comment: 37 pages, 6 figure
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