4,336 research outputs found
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
Detection of doubly-deuterated methanol in the solar-type protostar IRAS16293-2422
We report the first detection of doubly-deuterated methanol (CHD2OH), as well
as firm detections of the two singly-deuterated isotopomers of methanol (CH2DOH
and CH3OD), towards the solar-type protostar IRAS16293-2422. From the present
multifrequency observations, we derive the following abundance ratios:
[CHD2OH]/[CH3OH] = 0.2 +/- 0.1, [CH2DOH]/[CH3OH] = 0.9 +/- 0.3, [CH3OD]/[CH3OH]
= 0.04 +/- 0.02. The total abundance of the deuterated forms of methanol is
greater than that of its normal hydrogenated counterpart in the circumstellar
material of IRAS16293-2422, a circumstance not previously encountered.
Formaldehyde, which is thought to be the chemical precursor of methanol,
possesses a much lower fraction of deuterated isotopomers (~ 20%) with respect
to the main isotopic form in IRAS16293-2422. The observed fractionation of
methanol and formaldehyde provides a severe challenge to both gas-phase and
grain-surface models of deuteration. Two examples of the latter model are
roughly in agreement with our observations of CHD2OH and CH2DOH if the
accreting gas has a large (0.2-0.3) atomic D/H ratio. However, no gas-phase
model predicts such a high atomic D/H ratio, and hence some key ingredient
seems to be missing.Comment: 5 pages, 3 figure
Relativistic Coulomb Problem: Analytic Upper Bounds on Energy Levels
The spinless relativistic Coulomb problem is the bound-state problem for the
spinless Salpeter equation (a standard approximation to the Bethe--Salpeter
formalism as well as the most simple generalization of the nonrelativistic
Schr\"odinger formalism towards incorporation of relativistic effects) with the
Coulomb interaction potential (the static limit of the exchange of some
massless bosons, as present in unbroken gauge theories). The nonlocal nature of
the Hamiltonian encountered here, however, renders extremely difficult to
obtain rigorous analytic statements on the corresponding solutions. In view of
this rather unsatisfactory state of affairs, we derive (sets of) analytic upper
bounds on the involved energy eigenvalues.Comment: 12 pages, LaTe
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
The matrix factorisations of the D-model
The fundamental matrix factorisations of the D-model superpotential are found
and identified with the boundary states of the corresponding conformal field
theory. The analysis is performed for both GSO-projections. We also comment on
the relation of this analysis to the theory of surface singularities and their
orbifold description.Comment: 23 pages, LaTe
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
Equivalences between GIT quotients of Landau-Ginzburg B-models
We define the category of B-branes in a (not necessarily affine)
Landau-Ginzburg B-model, incorporating the notion of R-charge. Our definition
is a direct generalization of the category of perfect complexes. We then
consider pairs of Landau-Ginzburg B-models that arise as different GIT
quotients of a vector space by a one-dimensional torus, and show that for each
such pair the two categories of B-branes are quasi-equivalent. In fact we
produce a whole set of quasi-equivalences indexed by the integers, and show
that the resulting auto-equivalences are all spherical twists.Comment: v3: Added two references. Final version, to appear in Comm. Math.
Phy
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
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
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