Disk Instantons, Mirror Symmetry and the Duality Web

By Mina Aganagic, A. Klemm, C. Vafa. 2001

345 citations recorded by the source corpus.

We apply the methods recently developed for computation of type IIA disk instantons using mirror symmetry to a large class of D-branes wrapped over Lagrangian cycles of non-compact Calabi-Yau 3-folds. Along the way we clarify the notion of “flat coordinates” for the boundary theory. We also discover an integer IR ambiguity needed to define the quantum theory of D-branes wrapped over non-compact Lagrangian submanifolds. In the large N dual Chern-Simons theory, this ambiguity is mapped to the UV choice of the framing of the knot. In a type IIB dual description involving (p; q) 5-branes, disk instantons of type IIA get mapped to (p; q) string instantons. The M-theory lift of these results lead to computation of superpotential terms generated by M2 brane instantons wrapped over 3-cycles of certain manifolds of G2 holonomy

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e9ec8522b0b9a77b231c274fa7e9d26b542a396a

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Citations in the corpus

Topological Strings from Quantum Mechanics (2014, background): “The resulting parametrization has a group of symmetries given by transformations of the form [30], ( x p ) → G ( x p ) , G ∈ SL(2,Z).”
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].”
Worldsheet derivation of a large N duality (2002, background): “As noted in [30,31,32], F (C) 0,1 is given by the integral of the top holomorphic form bounding the brane.”
Quantum geometry of refined topological strings (2011, background): “dũ ũ S ′ n [62], to ensure that the odd sector in ~ drops out.”
Non-perturbative effects and the refined topological string (2013, background): “This implies that the factor (QI/zI) 1 2 appearing in the open flat coordinate, which represents the instanton corrections to the disk amplitude [54], has the following product expression ( QI zI ) 1 2 = ∏”
Hurwitz numbers, matrix models and enumerative geometry (2007, methodology): “In particular, we review the proposal of [M, BKMP] that the one-leg, framed topological vertex obeys a similar set of recursion relations by using the mirror geometry first found in [ AKV ].”
Remodeling the B-Model (2007, methodology): “The closed string parameters can be fixed in each large radius patch by the methods of [5], which are reviewed in the next section.”
The Topological Vertex (2003, methodology): “(3.7)”
Framed knots at large N (2001, methodology): “However, it was discovered in [8], that there is an inherent ambiguity in the open topological string amplitude related to the IR geometry of the D-brane.”
All Loop Topological String Amplitudes from Chern-Simons Theory (2002, background): “The role of framing in topological string theory was discovered in [7] in a closely related context and studied subsequently in [8,41,42].”
Vortex Counting and Lagrangian 3-Manifolds (2010, background): “lated to the choice of three-dimensional Chern-Simons coupling. This is done by including an extra toric degeneration locus, in a plane parallel to but disjoint from that of the initial toric diagram [35, 32]. The extra degeneration locus compacties the Lagrangian brane to an S3. We will always chos”
Orientifolds of K3 and Calabi-Yau manifolds with intersecting D-branes (2002, neutral): “Keywords: Superstring Vacua, D-branes, Supersymmetry Breaking. c© SISSA/ISAS 2002 http://jhep.sissa.it/archive/papers/jhep072002026/jhep072002026.pdf J H E P 0 7 ( 2 0 0 2 ) 0 2 6 Contents”
Torus Knots and Mirror Symmetry (2011, background): “As we will show in this paper, the B-model geometry corresponding to a (Q,P ) torus knot is simply given by a general Sl(2,Z) transformation of the spectral curve describing the resolved conifold.”
Topological M-theory as unification of form theories of gravity (2004, background): “This way of defining a topological M-theory on G2 was suggested in [12,13].”