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

HOT-SPOT PHENOMENON IN PV SYSTEMS WITH OVERHEAD LINES PARTIAL SHADING

This paper deals with the occurrence of hot-spot phenomenon in photovoltaic systems under PV partial shadowing. In an experimental campaign, the hot-spot phenomenon was revealed on a PV installation in Italy, caused my medium voltage overhead lines shadowing the PV cells. Starting from these practice case studies, at the SolarTech laboratory of Politecnico di Milano, the conditions for hot-spot phenomenon occurrence due to the overhead lines shading the PV cells were reproduced. Two experimental campaigns were carried out to investigate the current-voltage and power-voltage characteristics, and the energy production. In each experimental campaign, the built shadowing structure was considered fixed, and different shadowing conditions were created based on the natural displacement of the sun. Still, for occurring the hot- spot phenomenon during the laboratory tests, more PV modules must be connected in parallel

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

Kahler Potential for M-theory on a G_2 Manifold

We compute the moduli Kahler potential for M-theory on a compact manifold of G_2 holonomy in a large radius approximation. Our method relies on an explicit G_2 structure with small torsion, its periods and the calculation of the approximate volume of the manifold. As a verification of our result, some of the components of the Kahler metric are computed directly by integration over harmonic forms. We also discuss the modification of our result in the presence of co-dimension four singularities and derive the gauge-kinetic functions for the massless gauge fields that arise in this case.Comment: 31 pages, Latex. Altered discussion of truncation of field content, some typos corrected and references added. Version to appear in Phys. Rev .

Constructing Gauge Theory Geometries from Matrix Models

We use the matrix model -- gauge theory correspondence of Dijkgraaf and Vafa in order to construct the geometry encoding the exact gaugino condensate superpotential for the N=1 U(N) gauge theory with adjoint and symmetric or anti-symmetric matter, broken by a tree level superpotential to a product subgroup involving U(N_i) and SO(N_i) or Sp(N_i/2) factors. The relevant geometry is encoded by a non-hyperelliptic Riemann surface, which we extract from the exact loop equations. We also show that O(1/N) corrections can be extracted from a logarithmic deformation of this surface. The loop equations contain explicitly subleading terms of order 1/N, which encode information of string theory on an orientifolded local quiver geometry.Comment: 52 page

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

Quivers from Matrix Factorizations

We discuss how matrix factorizations offer a practical method of computing the quiver and associated superpotential for a hypersurface singularity. This method also yields explicit geometrical interpretations of D-branes (i.e., quiver representations) on a resolution given in terms of Grassmannians. As an example we analyze some non-toric singularities which are resolved by a single CP1 but have "length" greater than one. These examples have a much richer structure than conifolds. A picture is proposed that relates matrix factorizations in Landau-Ginzburg theories to the way that matrix factorizations are used in this paper to perform noncommutative resolutions.Comment: 33 pages, (minor changes

On the monoidal structure of matrix bi-factorisations

We investigate tensor products of matrix factorisations. This is most naturally done by formulating matrix factorisations in terms of bimodules instead of modules. If the underlying ring is C[x_1,...,x_N] we show that bimodule matrix factorisations form a monoidal category. This monoidal category has a physical interpretation in terms of defect lines in a two-dimensional Landau-Ginzburg model. There is a dual description via conformal field theory, which in the special case of W=x^d is an N=2 minimal model, and which also gives rise to a monoidal category describing defect lines. We carry out a comparison of these two categories in certain subsectors by explicitly computing 6j-symbols.Comment: 43 pages; v2: corrected a mistake in sec. 1 and app. A.1, the results are unaffected; v3: minor change

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

Matrix Model Description of Laughlin Hall States

We analyze Susskind's proposal of applying the non-commutative Chern-Simons theory to the quantum Hall effect. We study the corresponding regularized matrix Chern-Simons theory introduced by Polychronakos. We use holomorphic quantization and perform a change of matrix variables that solves the Gauss law constraint. The remaining physical degrees of freedom are the complex eigenvalues that can be interpreted as the coordinates of electrons in the lowest Landau level with Laughlin's wave function. At the same time, a statistical interaction is generated among the electrons that is necessary to stabilize the ground state. The stability conditions can be expressed as the highest-weight conditions for the representations of the W-infinity algebra in the matrix theory. This symmetry provides a coordinate-independent characterization of the incompressible quantum Hall states.Comment: 31 pages, large additions on the path integral and overlaps, and on the W-infinity symmetr