15 research outputs found
Algorithmic deformation of matrix factorisations
Branes and defects in topological Landau-Ginzburg models are described by
matrix factorisations. We revisit the problem of deforming them and discuss
various deformation methods as well as their relations. We have implemented
these algorithms and apply them to several examples. Apart from explicit
results in concrete cases, this leads to a novel way to generate new matrix
factorisations via nilpotent substitutions, and to criteria whether boundary
obstructions can be lifted by bulk deformations.Comment: 30 page
Remarks on quiver gauge theories from open topological string theory
We study effective quiver gauge theories arising from a stack of D3-branes on certain Calabi-Yau singularities. Our point of view is a first principle approach via open topological string theory. This means that we construct the natural A-infinity-structure of open string amplitudes in the associated D-brane category. Then we show that it precisely reproduces the results of the method of brane tilings, without having to resort to any effective field theory computations. In particular, we prove a general and simple formula for effective superpotentials
Defect Perturbations in Landau-Ginzburg Models
Perturbations of B-type defects in Landau-Ginzburg models are considered. In
particular, the effect of perturbations of defects on their fusion is analyzed
in the framework of matrix factorizations. As an application, it is discussed
how fusion with perturbed defects induces perturbations on boundary conditions.
It is shown that in some classes of models all boundary perturbations can be
obtained in this way. Moreover, a universal class of perturbed defects is
constructed, whose fusion under certain conditions obey braid relations. The
functors obtained by fusing these defects with boundary conditions are twist
functors as introduced in the work of Seidel and Thomas.Comment: 46 page
Generalized Berezin quantization, Bergman metrics and fuzzy laplacians
We study extended Berezin and Berezin-Toeplitz quantization for compact Kähler manifolds, two related quantization procedures which provide a general framework for approaching the construction of fuzzy compact Kähler geometries. Using this framework, we show that a particular version of generalized Berezin quantization, which we baptize ''Berezin-Bergman quantization'', reproduces recent proposals for the construction of fuzzy Kähler spaces. We also discuss how fuzzy laplacians can be defined in our general framework and study a few explicit examples. Finally, we use this approach to propose a general explicit definition of fuzzy scalar field theory on compact Kähler manifolds. © 2008 SISSA
Strong Homotopy Lie Algebras, Generalized Nahm Equations and Multiple M2-branes
We review various generalizations of the notion of Lie algebras, in particular those appearing in the recently proposed Bagger-Lambert-Gustavsson model, and study their interrelations. We find that Filippov's n-Lie algebras are a special case of strong homotopy Lie algebras. Furthermore, we define a class of homotopy Maurer-Cartan equations, which contains both the Nahm and the Basu-Harvey equations as special cases. Finally, we show how the super Yang-Mills equations describing a Dp-brane and the Bagger-Lambert-Gustavsson equations supposedly describing M2-branes can be rewritten as homotopy Maurer-Cartan equations, as well