Mirror symmetry, D-branes and counting holomorphic discs
By Mina Aganagic, C. Vafa. 2000
470 citations recorded by the source corpus.
We consider a class of special Lagrangian subspaces of Calabi-Yau manifolds and identify their mirrors, using the recent derivation of mirror symmetry, as certain holomorphic varieties of the mirror geometry. This transforms the counting of holomorphic disc instantons ending on the Lagrangian submanifold to the classical Abel-Jacobi map on the mirror. We recover some results already anticipated as well as obtain some highly non-trivial new predictions.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/dfab173dc18dfb62f37105f140c04a828f1fef3e
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- A large N duality via a geometric transition (2001, background): “As discussed in [19] such a D-brane gives rise to an additional spacetime superpotential”
- Orientifolds of K3 and Calabi-Yau manifolds with intersecting D-branes (2002, background): “As a new example we derive a non-supersymmetric Standard-like Model from an orientifold of type IIA on the quintic Calabi-Yau 3-fold with wrapped D6-branes.”
- Remodeling the B-Model (2007, methodology): “The Lagrangian submanifolds that we will be interested in were constructed by [6], as a generalization of Harvey-Lawson special Lagrangians [30] in C(3).”
- Framed knots at large N (2001, methodology): “The framed unknot and the B-model disk amplitude The open Gromov-Witten invariants for g = 0, h = 1 (disk amplitudes) can also be computed in the B-model by using the techniques of [7][8].”
- Four-dimensional string compactifications with D-branes, orientifolds and fluxes (2006, methodology): “The string tree-level superpotential, which is solely generated by world-sheet instantons, has been discussed in [214, 215, 216, 217].”
- Vortex Counting and Lagrangian 3-Manifolds (2010, background): “) corresponds to a simple special Lagrangian submanifold M˘=S1 R2 invariant under the toric symmetry of X. Such toric Lagrangian submanifolds have been extensively used in the physics literature (cf. [30, 31, 32]), so we can borrow many results to apply to our problem. One way to see this is to star”
- A& B model approaches to surface operators and Toda thoeries (2010, methodology): “The disk amplitude [21, 22] is obtained from the line integral of the one–form on the mirror curve, obtained by solving y as a function of x in H(x, y; u) = 0:”
- Matrix models, geometric engineering and elliptic genera (2003, background): “Such a 3-cycle is Lagrangian and can be used to define the boundary conditions for the open topological strings [51,52].”
- d-Brane Instantons in Type II Orientifolds (2009, background): “The superpotential which the non-trivial fibration induces for these adjoints can be computed as follows [125, 126].”
- Open string amplitudes and large order behavior in topological string theory (2006, methodology): “As shown in [7, 5], they are simply given by”
- Quantum geometry of refined topological strings (2011, methodology): “This is mirror to the A-model partition function, when one includes instanton corrections along with the Chern-Simons functional [16, 19].”
- Supersymmetric Intersecting Branes on the Type IIA T6/Bbb Z4 Orientifold (2002, background): “From general arguments for open string models with N = 1 supersymmetry, it is known that the complex structure moduli only appear in the D-term potential, whereas the Kähler moduli only appear in the F-term potential [63,64,66].”
- Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c = 1 Matrix Models (2009, background): “In this case, the disk amplitude with (mirror of) toric–brane boundary conditions may be written, in terms of the mirror curve25, as [61, 62] A (0) 1 (x) = ∫ x ds y(s).”