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89
LandauGinzburg Realization of Open String TFT
, 2003
"... We investigate Btype topological LandauGinzburg theory with one variable, with D2brane boundary conditions. The allowed brane configurations are determined in terms of the possible factorizations of the superpotential, and compute the corresponding open string chiral rings. These are characterized ..."
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Cited by 64 (14 self)
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We investigate Btype topological LandauGinzburg theory with one variable, with D2brane boundary conditions. The allowed brane configurations are determined in terms of the possible factorizations of the superpotential, and compute the corresponding open string chiral rings. These are characterized by bosonic and fermionic generators that satisfy certain relations. Moreover we show that the disk correlators, being continuous functions of deformation parameters, satisfy the topological sewing constraints, thereby proving consistency of the theory. In addition we show that the open string LG model is, in its content, equivalent to a certain triangulated category introduced by Kontsevich, and thus may be viewed as a concrete physical realization of it.
Topological Correlators in Landau–Ginzburg Models with Boundaries
 Adv. Theor. Math. Phys
"... We compute topological correlators in LandauGinzburg models on a Riemann surface with arbitrary number of handles and boundaries. The boundaries may correspond to arbitrary topological Dbranes of type B. We also allow arbitrary operator insertions on the boundary and in the bulk. The answer is giv ..."
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Cited by 63 (3 self)
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We compute topological correlators in LandauGinzburg models on a Riemann surface with arbitrary number of handles and boundaries. The boundaries may correspond to arbitrary topological Dbranes of type B. We also allow arbitrary operator insertions on the boundary and in the bulk. The answer is given by an explicit formula which can be regarded as an openstring generalization of C. Vafa’s formula for closedstring topological correlators. We discuss how to extend our results to the case of LandauGinzburg orbifolds.
Mirror symmetry for weighted projective planes and their noncommutative deformations
, 2004
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Derived categories of coherent sheaves and triangulated categories of singularities
, 2005
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On the boundary coupling of topological LandauGinzburg models,” arXiv:hepth/0312286
"... Abstract: I propose a general form for the boundary coupling of Btype topological LandauGinzburg models. In particular, I show that the relevant background in the open string sector is a (generally nonAbelian) superconnection of type (0, 1) living in a complex superbundle defined on the target sp ..."
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Cited by 39 (2 self)
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Abstract: I propose a general form for the boundary coupling of Btype topological LandauGinzburg models. In particular, I show that the relevant background in the open string sector is a (generally nonAbelian) superconnection of type (0, 1) living in a complex superbundle defined on the target space, which I allow to be a noncompact CalabiYau 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 LandauGinzburg potential times the identity section of the underlying superbundle. This provides the target space equations of motion for the open topological model. Contents
DBranes in Topological Minimal Models: The LandauGinzburg Approach
"... Abstract. We study Dbranes in topologically twisted N = 2 minimal models using the LandauGinzburg realization. In the cases of A and Dtype minimal models we provide what we believe is an exhaustive list of topological branes and compute the corresponding boundary OPE algebras as well as all disk ..."
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Cited by 36 (0 self)
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Abstract. We study Dbranes in topologically twisted N = 2 minimal models using the LandauGinzburg realization. In the cases of A and Dtype minimal models we provide what we believe is an exhaustive list of topological branes and compute the corresponding boundary OPE algebras as well as all disk correlators. We also construct examples of topological branes in Etype minimal models. We compare our results with the boundary state formalism, where possible, and find agreement. 1.
Dbranes on CalabiYau manifolds
, 2004
"... In this review we study BPS Dbranes on Calabi–Yau threefolds. Such Dbranes naturally divide into two sets called Abranes and Bbranes which are most easily understood from topological field theory. The main aim of this paper is to provide a selfcontained guide to the derived category approach to ..."
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Cited by 35 (7 self)
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In this review we study BPS Dbranes on Calabi–Yau threefolds. Such Dbranes naturally divide into two sets called Abranes and Bbranes which are most easily understood from topological field theory. The main aim of this paper is to provide a selfcontained guide to the derived category approach to Bbranes and the idea of Πstability. We argue that this mathematical machinery is hard to avoid for a proper understanding of Bbranes. Abranes and Bbranes are related in a very complicated and interesting way which ties in with the “homological mirror symmetry ” conjecture of Kontsevich. We motivate and exploit this form of mirror symmetry. The examples of the quintic 3fold, flops and orbifolds are discussed at some length. In the latter
The stable derived category of a Noetherian scheme
 Compos. Math
"... Dedicated to Claus Michael Ringel on the occasion of his sixtieth birthday. Abstract. For a noetherian scheme, we introduce its unbounded stable derived category. This leads to a recollement which reflects the passage from the bounded derived category of coherent sheaves to the quotient modulo the s ..."
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Cited by 34 (5 self)
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Dedicated to Claus Michael Ringel on the occasion of his sixtieth birthday. Abstract. For a noetherian scheme, we introduce its unbounded stable derived category. This leads to a recollement which reflects the passage from the bounded derived category of coherent sheaves to the quotient modulo the subcategory of perfect complexes. Some applications are included, for instance an analogue of maximal CohenMacaulay approximations, a construction of Tate cohomology, and an extension of the classical Grothendieck duality. In addition, the relevance of the stable derived category in modular representation theory is indicated.
Duality and equivalence of module categories in noncommutative geometry II: Mukai . . .
, 2006
"... This is the second in a series of papers intended to set up a framework to study categories of modules in the context of noncommutative geometries. In [3] we introduced ..."
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Cited by 28 (4 self)
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This is the second in a series of papers intended to set up a framework to study categories of modules in the context of noncommutative geometries. In [3] we introduced
Fractional branes in LandauGinzburg orbifolds
 ADV. THEOR. MATH. PHYS
, 2004
"... We construct fractional branes in LandauGinzburg orbifold categories and study their behavior under marginal closed string perturbations. This approach is shown to be more general than the rational boundary state construction. In particular we find new Dbranes on the quintic – such as a single D0 ..."
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Cited by 25 (0 self)
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We construct fractional branes in LandauGinzburg orbifold categories and study their behavior under marginal closed string perturbations. This approach is shown to be more general than the rational boundary state construction. In particular we find new Dbranes on the quintic – such as a single D0brane – which are not restrictions of bundles on the ambient projective space. We also exhibit a family of deformations of the D0brane in the LandauGinzburg category parameterized by points on the Fermat quintic.