34 research outputs found
Localization and traces in open-closed topological Landau-Ginzburg models
We reconsider the issue of localization in open-closed B-twisted
Landau-Ginzburg models with arbitrary Calabi-Yau target. Through careful
analsysis of zero-mode reduction, we show that the closed model allows for a
one-parameter family of localization pictures, which generalize the standard
residue representation. The parameter which indexes these pictures
measures the area of worldsheets with topology, with the residue
representation obtained in the limit of small area. In the boundary sector, we
find a double family of such pictures, depending on parameters and
which measure the area and boundary length of worldsheets with disk
topology. We show that setting and varying interpolates
between the localization picture of the B-model with a noncompact target space
and a certain residue representation proposed recently. This gives a complete
derivation of the boundary residue formula, starting from the explicit
construction of the boundary coupling. We also show that the various
localization pictures are related by a semigroup of homotopy equivalences.Comment: 36 page
A retrospective review of fatal electrocution cases at Tygerberg Forensic Pathology Services, Cape Town, South Africa, over the 5-year period 1 January 2008 - 31 December 2012
Background. Electrocution as a cause of death has been discussed extensively in the international literature. However, research on this topic in South Africa (SA) is scarce.Objectives. To address the need for further research in this field and emphasise the necessity for preventive measures by determining the demographic and pathological profile of fatal electrocution cases seen in the Tygerberg Forensic Pathology Services, Western Cape Province, SA.Methods. The study was a retrospective and descriptive case series of all the cases of death secondary to electrocution referred to the study facility from 1 January 2008 to 31 December 2012.Results. A total of 39 cases were included. Ten victims (25.6%) were aged <13 years. The geographical area most affected by electrocution deaths was the informal settlement Khayelitsha (56.4% of cases). The primary injuries described were mainly burn wounds (34 cases, 87.2%) and abrasions (4 cases, 10.3%). Most injuries were to the upper limbs. Unfortunately, the results pertaining specifically to the pathology of electrical burn wounds were inconclusive.Conclusions. In view of discrepancies found in the reporting of electrical burn wounds, a standardised system for classifying these wounds is suggested. Although electrocution-related mortality is not a leading cause of death in high-prevalence areas, awareness should be raised
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
Graded D-branes and skew-categories
I describe extended gradings of open topological field theories in two
dimensions in terms of skew categories, proving a result which alows one to
translate between the formalism of graded open 2d TFTs and equivariant cyclic
categories. As an application of this formalism, I describe the open 2d TFT of
graded D-branes in Landau-Ginzburg models in terms of an equivariant cyclic
structure on the triangulated category of `graded matrix factorizations'
introduced by Orlov. This leads to a specific conjecture for the Serre functor
on the latter, which generalizes results known from the minimal and Calabi-Yau
cases. I also give a description of the open 2d TFT of such models which
manifestly displays the full grading induced by the vector-axial R-symmetry
group.Comment: 37 page
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
Effective superpotentials for B-branes in Landau-Ginzburg models
We compute the partition function for the topological Landau-Ginzburg B-model
on the disk. This is done by treating the worldsheet superpotential
perturbatively. We argue that this partition function as a function of bulk and
boundary perturbations may be identified with the effective D-brane
superpotential in the target spacetime. We point out the relationship of this
approach to matrix factorizations. Using these methods, we prove a conjecture
for the effective superpotential of Herbst, Lazaroiu and Lerche for the A-type
minimal models. We also consider the Landau-Ginzburg theory of the cubic torus
where we show that the effective superpotential, given by the partition
function, is consistent with the one obtained by summing up disk instantons in
the mirror A-model. This is done by explicitly constructing the open-string
mirror map.Comment: 57p, 7 figs, harvma
Calculations for Mirror Symmetry with D-branes
We study normal functions capturing D-brane superpotentials on several one-
and two-parameter Calabi-Yau hypersurfaces and complete intersections in
weighted projective space. We calculate in the B-model and interpret the
results using mirror symmetry in the large volume regime, albeit without
identifying the precise A-model geometry in all cases. We identify new classes
of extensions of Picard-Fuchs equations, as well as a novel type of topology
changing phase transition involving quantum D-branes. A 4-d domain wall which
is obtained in one region of closed string moduli space from wrapping a
four-chain interpolating between two Lagrangian submanifolds is, for other
values of the parameters, represented by a disk ending on a single Lagrangian.Comment: 42 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
D-brane Categories for Orientifolds -- The Landau-Ginzburg Case
We construct and classify categories of D-branes in orientifolds based on
Landau-Ginzburg models and their orbifolds. Consistency of the worldsheet
parity action on the matrix factorizations plays the key role. This provides
all the requisite data for an orientifold construction after embedding in
string theory. One of our main results is a computation of topological field
theory correlators on unoriented worldsheets, generalizing the formulas of Vafa
and Kapustin-Li for oriented worldsheets, as well as the extension of these
results to orbifolds. We also find a doubling of Knoerrer periodicity in the
orientifold context.Comment: 45 pages, 6 figure
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