Chern-Simons theory and topological strings

By Marcos Mariño. 2004

200 citations recorded by the source corpus.

A review of the relation between Chern-Simons gauge theory and topological string theory on noncompact Calabi-Yau spaces is given. This relation has made it possible to give an exact solution of topological string theory on these spaces to all orders in the string coupling constant. Here the focus is on the construction of this solution, which is encoded in the topological vertex, and the implications of the physics of string/gauge theory duality for knot theory and for the geometry of Calabi-Yau manifolds.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/1bfee8131371f5817974a0bfe11cb00f0eae13e5

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

In Nuclear and High Energy Physics

Citations in the corpus

Open string amplitudes and large order behavior in topological string theory (2006, methodology): “General recent references on topological strings include [54, 69, 59], to which we refer the reader for background material.”
Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories (2011, background): “79) A detailed explanation of the exact solution of CS theory would take us too far, and we refer the reader to the original paper [97] or to the presentation in [73] for more details.”
Remodeling the B-Model (2007, background): “The simplest test of the Ooguri–Vafa conjecture is the unknot, which corresponds to a toric D-brane in an outer edge of the resolved conifold (see for example [39] for details).”
Exact results for perturbative Chern-Simons theory with complex gauge group. (2009, background): “[16, 33] for excellent reviews) and with a wide range of applications, ranging from invariants of knots and 3manifolds [52] on one hand, to condensed matter physics [25, 39] and string theory [35] on the other.”
Explicit de Sitter flux vacua for global string models with chiral matter (2013, methodology): “or the interested reader. We also present explicit formulas for the period vector and the ux superpotential W ux in terms of the prepotential F. For more details we refer to standard references, e.g. [60, 22, 61]. We closely follow [62]. A.1 Periods as solutions to the Picard-Fuchs equations In this”
Les Houches lectures on matrix models and topological strings (2004, background): “For a detailed review of a similar story for the A string, we refer the reader to [54].”
Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c = 1 Matrix Models (2009, background): “The SU(N) Chern–Simons gauge theory on a generic three– manifold has been realized as a matrix model in [8]; see [58] for a review.”
Lectures on black holes, topological strings and quantum attractors (2006, background): “Other valuable reviews of topological string theory include [56, 57, 58, 59, 60].”
Hurwitz numbers, matrix models and enumerative geometry (2007, background): “A toric Calabi–Yau is necessarily noncompact, and can be represented by a toric diagram which encodes its fibration structure (see for example [ M1 ] for details).”
The Resurgence of Instantons in String Theory (2011, background): “ simply its set of GV integer invariants (and its Euler number if one is also to write down the constant map contribution). Expressed as a topological genus expansion one nds, at genus g, (see, e.g., [50, 47, 52] for partial expressions) F g(t i) = +X1 d i=1 8 < : jB 2gj 2g(2g 2)! n(d i) 0 + Xg h”
Partition functions of holographic minimal models (2011, methodology): “2) is similar to the Ooguri-Vafa operator [33] (see also [34, 35, 36]) that arises in the topological string computation of knot invariants.”