Remodeling the B-Model

By V. Bouchard, A. Klemm, Marcos Mariño, Sara Pasquetti. 2007

362 citations recorded by the source corpus.

We propose a complete, new formalism to compute unambiguously B-model open and closed amplitudes in local Calabi–Yau geometries, including the mirrors of toric manifolds. The formalism is based on the recursive solution of matrix models recently proposed by Eynard and Orantin. The resulting amplitudes are non-perturbative in both the closed and the open moduli. The formalism can then be used to study stringy phase transitions in the open/closed moduli space. At large radius, this formalism may be seen as a mirror formalism to the topological vertex, but it is also valid in other phases in the moduli space. We develop the formalism in general and provide an extensive number of checks, including a test at the orbifold point of Ap fibrations, where the amplitudes compute the ’t Hooft expansion of vevs of Wilson loops in Chern-Simons theory on lens spaces. We also use our formalism to predict the disk amplitude for the orbifold $${{mathbb {C}}^3 /{mathbb{Z}}_3}$$ .

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e6f32b5552e4429bf4838279eee06ff997835817

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Citations in the corpus

From Weak to Strong Coupling in ABJM Theory (2010, background): “1), or equivalently from the formalism of [59] (appropriately modified as in [60,61]).”
Torus Knots and Mirror Symmetry (2011, methodology): “The mirror of the resolved conifold can be described by the spectral curve (see [3,8]) H(U, V ) = V − c−1UV + cU − 1 = 0, (3.”
Quantum Riemann Surfaces in Chern-Simons Theory (2011, methodology): “The known methods for quantizing H(x, y) involve matrix models [24, 25], and express Ĥ(x̂, ŷ; q) not as a finite polynomial in its three arguments (cf.”
The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers (2009, methodology): “[2] V. Bouchard, A. Klemm, M. Mariño, and S. Pasquetti, Remodeling the B-model, Commun.”
Hurwitz numbers, matrix models and enumerative geometry (2007, methodology): “Note that after the appearance of [M, BKMP ], this line of thought was further refined in [DV], where a physical reinterpretation of the recursion relation directly in terms of the chiral boson theory was proposed.”
Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions (2007, background): “vertices, and as such is known to have an interpretation in terms of chiral bosons and fermions [64, 11, 77, 78 ].”
Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c = 1 Matrix Models (2009, background): “This topic has been extensively studied in the literature and we refer the reader to the recent developments [ 11 ,12] and references therein.”
Two-Sphere Partition Functions and Gromov–Witten Invariants (2012, background): “For instance, we expect that the expansion about an orbifold point in the quantum Kähler moduli space computes orbifold Gromov–Witten invariants [85–87], see Appendix A for the quintic partition function expanded around its Landau–Ginzburg orbifold”
A-polynomial, B-model, and quantization (2011, methodology): “One of such recent developments is the topological recursion of Eynard-Orantin [12] and its extension to curves in C∗ × C∗ called the “remodeling conjecture” [13, 14].”
Polynomial recursion formula for linear Hodge integrals (2009, background): “This gives the dimension of the Hurwitz scheme, i.e., the moduli space of all Hurwitz covers for a given genus and a profile [32, Section 7.3.2].”
The Resurgence of Instantons in String Theory (2011, background): “Moreover, this procedure later allowed for very interesting extensions of the proposal in [3] to more general topological string backgrounds, including duals of closed strings on mirrors of toric backgrounds [10, 11].”
The Ω Deformed B-model for Rigid N = 2 Theories (2011, background): “An explicit link between topological strings and matrix models was established in [27].”
Vortex Counting and Lagrangian 3-Manifolds (2010, background): “This is expected from the description of a surface operator as a Lagrangian brane in the open BPS theory, since such a Lagrangian brane is well-known to have a dual description as a free fermion field [54, 55, 56].”
Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings (2007, methodology): “ one obtains an algebraic equation for the C∗ variables X,Y , which leads to the mirror CY threefold (5.1). The advantage of writing the curve in the nonalgebraic form (5.10) is that, as explained in [6, 7], one can apply verbatim the standard matrix model technology that we use in this paper. The c”
Random matrices. (2015, methodology): “In particular, in 2008, the Bouchard–Klemm–Mariño–Pasquetti (BKMP) conjecture [18] (since then proved [19]) claimed that topological string amplitudes obey the same recursion relations as matrix models’ correlation functions.”
Invariants of spectral curves and intersection theory of moduli spaces of complex curves (2011, background): “More generally, it was initially proposed by Mariño [21] and refined by Bouchard– Klemm–Mariño–Pasquetti (BKMP) [4], that if we choose the spectral curve to be the mirror curve of a toric Calabi–Yau 3–fold X, then the W (g) n ’s should be generating functions for the Gromov–Witten invariants of X,”
Gromov–Witten invariants of ℙ1 and Eynard–Orantin invariants (2011, methodology): “Important examples of the Eynard-Orantin invariants, using different choices of (C, x, y), store intersection numbers over the moduli space of curves [5]; simple Hurwitz numbers [1, 3, 6]; a count of lattice points in the moduli space of curves [17]; and conjecturally local Gromov-Witten invariants ”
Topological Strings from Quantum Mechanics (2014, background): “It turns out [31, 32] that all the perturbative information about the B-model topological string on X̂ is encoded in the equation WX(e , e) = 0, (2.”
Nonperturbative effects and nonperturbative definitions in matrix models and topological strings (2008, background): “Of course, it would be even more interesting to find explicit difference equations for the topological string partition function on other Calabi–Yau targets, or to translate the matrix model results of [62, 9] in such a framework.”