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44
Opening Mirror Symmetry on the Quintic
, 2006
"... Aided by mirror symmetry, we determine the number of holomorphic disks ending on the real Lagrangian in the quintic threefold. The tension of the domainwall between the two vacua on the brane, which is the generating function for the open GromovWitten invariants, satisfies a certain extension of th ..."
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Cited by 60 (13 self)
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Aided by mirror symmetry, we determine the number of holomorphic disks ending on the real Lagrangian in the quintic threefold. The tension of the domainwall between the two vacua on the brane, which is the generating function for the open GromovWitten invariants, satisfies a certain extension of the PicardFuchs differential equation governing periods of the mirror quintic. We verify consistency of the monodromies under analytic continuation of the superpotential over the entire moduli space. We reproduce the first few instanton numbers by a localization computation directly in the Amodel, and check OoguriVafa integrality. This is the first exact result on open string mirror symmetry for a compact CalabiYau manifold.
On the boundary coupling of topological LandauGinzburg models
, 2003
"... 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, whi ..."
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Cited by 50 (3 self)
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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.
Noncommutative homotopy algebras associated with open strings
 REV. MATH. PHYS
, 2003
"... We discuss general properties of A∞algebras and their applications to the theory of open strings. The properties of cyclicity for A∞algebras are examined in detail. We prove the decomposition theorem, which is a stronger version of the minimal model theorem, for A∞algebras and cyclic A∞algebras a ..."
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Cited by 28 (5 self)
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We discuss general properties of A∞algebras and their applications to the theory of open strings. The properties of cyclicity for A∞algebras are examined in detail. We prove the decomposition theorem, which is a stronger version of the minimal model theorem, for A∞algebras and cyclic A∞algebras and discuss various consequences of it. In particular it is applied to classical open string field theories and it is shown that all classical open string field theories on a fixed conformal background are cyclic A∞isomorphic to each other. The same results hold for classical closed string field theories, whose algebraic structure is governed by cyclic L∞algebras.
Dbranes from Matrix Factorizations
 Comptes Rendus Physique 5 (2004) 1061–1070, hepth/0409204
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Hints for OffShell Mirror Symmetry in type II/Ftheory Compactifications
, 2009
"... We perform a Hodge theoretic study of parameter dependent families of Dbranes on compact Calabi–Yau manifolds in type II and Ftheory compactifications. Starting from a geometric GaussManin connection for B type branes we study the integrability and flatness conditions. The B model geometry define ..."
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Cited by 24 (4 self)
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We perform a Hodge theoretic study of parameter dependent families of Dbranes on compact Calabi–Yau manifolds in type II and Ftheory compactifications. Starting from a geometric GaussManin connection for B type branes we study the integrability and flatness conditions. The B model geometry defines an interesting ring structure of operators. For the mirror A model this indicates the existence of an openstring extension of the socalled A model connection, whereas the discovered ring structure should be part of the openstring A model quantum cohomology. We obtain predictions for genuine OoguriVafa invariants for Lagrangian branes on the quintic in P 4 that pass some nontrivial consistency checks. We discuss the lift of the brane compactifications to Ftheory on Calabi–Yau 4folds and the effective couplings in the effective supergravity action as determined by the N = 1 special geometry of the openclosed deformation space.
DBranes on CalabiYau Manifolds and Superpotentials
, 2002
"... We show how to compute terms in an expansion of the worldvolume superpotential for fairly general Dbranes on the quintic CalabiYau using linear sigma model techniques, and show in examples that this superpotential captures the geometry and obstruction theory of bundles and sheaves on this Calabi ..."
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Cited by 24 (4 self)
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We show how to compute terms in an expansion of the worldvolume superpotential for fairly general Dbranes on the quintic CalabiYau using linear sigma model techniques, and show in examples that this superpotential captures the geometry and obstruction theory of bundles and sheaves on this CalabiYau.
Calculations for Mirror Symmetry with Dbranes
, 2009
"... We study normal functions capturing Dbrane superpotentials on several one and twoparameter CalabiYau hypersurfaces and complete intersections in weighted projective space. We calculate in the Bmodel and interpret the results using mirror symmetry in the large volume regime, albeit without ident ..."
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Cited by 22 (2 self)
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We study normal functions capturing Dbrane superpotentials on several one and twoparameter CalabiYau hypersurfaces and complete intersections in weighted projective space. We calculate in the Bmodel and interpret the results using mirror symmetry in the large volume regime, albeit without identifying the precise Amodel geometry in all cases. We identify new classes of extensions of PicardFuchs equations, as well as a novel type of topology changing phase transition involving quantum Dbranes. A 4d domain wall which is obtained in one region of closed string moduli space from wrapping a fourchain interpolating between two Lagrangian submanifolds is, for other