71 research outputs found
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
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