Localized Tachyons and the Quantum McKay Correspondence

The condensation of closed string tachyons localized at the fixed point of a C^d/\Gamma orbifold can be studied in the framework of renormalization group flow in a gauged linear sigma model. The evolution of the Higgs branch along the flow describes a resolution of singularities via the process of tachyon condensation. The study of the fate of D-branes in this process has lead to a notion of a ``quantum McKay correspondence.'' This is a hypothetical correspondence between fractional branes in an orbifold singularity in the ultraviolet with the Coulomb and Higgs branch branes in the infrared. In this paper we present some nontrivial evidence for this correspondence in the case C^2/Z_n by relating the intersection form of fractional branes to that of ``Higgs branch branes,'' the latter being branes which wrap nontrivial cycles in the resolved space.Comment: 25 pages; harvma

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 $\lambda$ which indexes these pictures measures the area of worldsheets with $S^2$ 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 $\lambda$ and $\mu$ which measure the area and boundary length of worldsheets with disk topology. We show that setting $\mu=0$ and varying $\lambda$ 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

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

On the boundary coupling of topological Landau-Ginzburg models

I propose a general form for the boundary coupling of B-type topological Landau-Ginzburg models. In particular, I show that the relevant background in the open string sector is a (generally non-Abelian) superconnection of type (0,1) living in a complex superbundle defined on the target space, which I allow to be a non-compact Calabi-Yau manifold. This extends and clarifies previous proposals. Generalizing an argument due to Witten, I show that BRST invariance of the partition function on the worldsheet amounts to the condition that the (0,<= 2) part of the superconnection's curvature equals a constant endomorphism plus the Landau-Ginzburg potential times the identity section of the underlying superbundle. This provides the target space equations of motion for the open topological model.Comment: 21 page

Matrix Factorizations, Minimal Models and Massey Products

We present a method to compute the full non-linear deformations of matrix factorizations for ADE minimal models. This method is based on the calculation of higher products in the cohomology, called Massey products. The algorithm yields a polynomial ring whose vanishing relations encode the obstructions of the deformations of the D-branes characterized by these matrix factorizations. This coincides with the critical locus of the effective superpotential which can be computed by integrating these relations. Our results for the effective superpotential are in agreement with those obtained from solving the A-infinity relations. We point out a relation to the superpotentials of Kazama-Suzuki models. We will illustrate our findings by various examples, putting emphasis on the E_6 minimal model.Comment: 32 pages, v2: typos corrected, v3: additional comments concerning the bulk-boundary crossing constraint, some small clarifications, typo

Models for Modules

We recall the structure of the indecomposable sl(2) modules in the Bernstein-Gelfand-Gelfand category O. We show that all these modules can arise as quantized phase spaces of physical models. In particular, we demonstrate in a path integral discretization how a redefined action of the sl(2) algebra over the complex numbers can glue finite dimensional and infinite dimensional highest weight representations into indecomposable wholes. Furthermore, we discuss how projective cover representations arise in the tensor product of finite dimensional and Verma modules and give explicit tensor product decomposition rules. The tensor product spaces can be realized in terms of product path integrals. Finally, we discuss relations of our results to brane quantization and cohomological calculations in string theory.Comment: 18 pages, 6 figure

Biomass burning and pollution aerosol over North America: Organic components and their influence on spectral optical properties and humidification response

Thermal analysis of aerosol size distributions provided size resolved volatility up to temperatures of 400°C during extensive flights over North America (NA) for the INTEX/ICARTT experiment in summer 2004. Biomass burning and pollution plumes identified from trace gas measurements were evaluated for their aerosol physiochemical and optical signatures. Measurements of soluble ionic mass and refractory black carbon (BC) mass, inferred from light absorption, were combined with volatility to identify organic carbon at 400°C (VolatileOC) and the residual or refractory organic carbon, RefractoryOC. This approach characterized distinct constituent mass fractions present in biomass burning and pollution plumes every 5–10 min. Biomass burning, pollution and dust aerosol could be stratified by their combined spectral scattering and absorption properties. The “nonplume” regional aerosol exhibited properties dominated by pollution characteristics near the surface and biomass burning aloft. VolatileOC included most water-soluble organic carbon. RefractoryOC dominated enhanced shortwave absorption in plumes from Alaskan and Canadian forest fires. The mass absorption efficiency of this RefractoryOC was about 0.63 m2 g−1 at 470 nm and 0.09 m2 g−1 at 530 nm. Concurrent measurements of the humidity dependence of scattering, γ, revealed the OC component to be only weakly hygroscopic resulting in a general decrease in γ with increasing OC mass fractions. Under ambient humidity conditions, the systematic relations between physiochemical properties and γ lead to a well-constrained dependency on the absorption per unit dry mass for these plume types that may be used to challenge remotely sensed and modeled optical properties

Chern-Simons as a geometrical set up for three dimensional gauge theories

Three dimensional Yang-Mills gauge theories in the presence of the Chern-Simons action are seen as being generated by the pure topological Chern-Simons term through nonlinear covariant redefinitions of the gauge fieldComment: 26 pages, latex2

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

A comparison of similar aerosol measurements made on the NASA P3-B, DC-8, and NSF C-130 aircraft during TRACE-P and ACE-Asia

Two major aircraft experiments occurred off the Pacific coast of Asia during spring 2001: the NASA sponsored Transport and Chemical Evolution over the Pacific (TRACE-P) and the National Science Foundation (NSF) sponsored Aerosol Characterization Experiment-Asia (ACE-Asia). Both experiments studied emissions from the Asian continent (biomass burning, urban/industrial pollution, and dust). TRACE-P focused on trace gases and aerosol during March/April and was based primarily in Hong Kong and Yokota Air Force Base, Japan, and involved two aircraft: the NASA DC-8 and the NASA P3-B. ACE-Asia focused on aerosol and radiation during April/May and was based in Iwakuni Marine Corps Air Station, Japan, and involved the NSF C-130. This paper compares aerosol measurements from these aircraft including aerosol concentrations, size distributions (and integral properties), chemistry, and optical properties. Best overall agreement (generally within RMS instrumental uncertainty) was for physical properties of the submircron aerosol, including condensation nuclei concentrations, scattering coefficients, and differential mobility analyzer and optical particle counter (OPC) accumulation mode size distributions. Larger differences (typically outside of the RMS uncertainty) were often observed for parameters related to the supermicron aerosols (total scattering and absorption coefficients, coarse mode Forward Scattering Spectrometer Probe and OPC size distributions/integral properties, and soluble chemical species usually associated with the largest particles, e.g., Na+, Cl−, Ca2+, and Mg2+), where aircraft sampling is more demanding. Some of the observed differences reflect different inlets (e.g., low-turbulence inlet enhancement of coarse mode aerosol), differences in sampling lines, and instrument configuration and design. Means and variances of comparable measurements for horizontal legs were calculated, and regression analyses were performed for each platform and allow for an assessment of instrument performance. These results provide a basis for integrating aerosol data from these aircraft platforms for both the TRACE-P and ACE-Asia experiments