Matrix models, topological strings, and supersymmetric gauge theories

By R. Dijkgraaf, C. Vafa. 2002

704 citations recorded by the source corpus.

We show that B-model topological strings on local Calabi–Yau threefolds are large-N duals of matrix models, which in the planar limit naturally give rise to special geometry. These matrix models directly compute F-terms in an associated N=1 supersymmetric gauge theory, obtained by deforming N=2 theories by a superpotential term that can be directly identified with the potential of the matrix model. Moreover by tuning some of the parameters of the geometry in a double scaling limit we recover (p,q) conformal minimal models coupled to 2d gravity, thereby relating non-critical string theories to type II superstrings on Calabi–Yau backgrounds.

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

View Paper: https://www.semanticscholar.org/paper/97b192f5c66d320ad02adb3f77314980dcd1bab8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Matrix eigenvalue model: Feynman graph technique for all genera (2006, methodology): “…Mathematical Institute, ITEP, and Laboratoire Poncelet, Moscow, Russia and B. Eynardb SPhT, CEA, Saclay, France SPhT-T06/017 ITEP/TH-06/06 We present the diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with arbitrary power β by the…”
SUPERCONFORMAL FIELD THEORIES (2005, neutral): “In flat space this sector is only partly described by quantum mechanics [5], actually it is not quantum mechanics, but a matrix integral.”
JT gravity as a matrix integral (2019, neutral): “See, for example, [56, 57, 32].”
Algebraic Curve for the SO(6) Sector of AdS/CFT (2004, neutral): “ar X ∗Membre de l’Institut Universitaire de France”
Open string amplitudes and large order behavior in topological string theory (2006, background): “In the local CY backgrounds of [28] the B-model reduces to a matrix model for a Hermitian matrix M , and open string amplitudes have the following interpretation.”
Matrix model as a mirror of Chern-Simons theory (2002, methodology): “Above, Ω = dvdzduz is the holomorphic three-form on Y 5.”
Supersymmetry Breaking from a Calabi-Yau Singularity (2005, neutral): “Next, turning on Fayet-Iliopoulos terms in the field theory, we show that the theory should confine in the infrared.”
Topological String Theory on Compact Calabi–Yau: Modularity and Boundary Conditions (2006, background): “- [1] or large N-techniques [2] and has intriguing connections to Chern-Simons theory [3], open-closed string duality [4], matrix models [5], integrable hierarchies of non-critical string theory [6] and 2d Yang-Mills theory [7].”
Chiral Rings and Anomalies in Supersymmetric Gauge Theory (2002, neutral): “And we know the contribution of this gauge theory to the effective superpotential – it is the sum of Veneziano-Yankielowicz superpotentials (1.10) for each factor H(Si) = ∑ i NiH(Si) ∂H(Si) ∂Si = Si(1− lnSi) (4.35) Thus, we might conclude that the complete effective superpotential has the constant o”
Liouville Field Theory — A decade after the revolution (2004, methodology): “This may seem rather complicated and less efficient if we are only interested in the double scaling limit, but this method has a lot of applications including the recent Dijkgraaf-Vafa conjecture [90, 91, 92], [93, 94, 95].”
Topological Strings and Integrable Hierarchies (2003, background): “For compact branes, as has been argued before [4,5] the topological B-model for the class of CY given by (1.”
Knot Homology from Refined Chern-Simons Theory (2011, methodology): “In the topological string the operation of obtaining the partition function on Y from sewing partition functions on YL an YR is familiar, see for example [49,44,59].”
Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity (2019, methodology): “The rules for including D-brane boundaries do not have a clear origin in gravity; we must rely upon the matrix integral description of JT gravity to understand how to properly (31)These branes are also closely related to branes in topological string theories described by matrix models [64, 65, 66, 6”
Higher rank Wilson loops from a matrix model (2006, background): “sian model saddle point conﬁguration wherein the eigenvalues condense onto a cut in the complex eigenvalue plane with a spectral density characterised by the Wigner semi-circle distribution (see e.g. [25] and references therein) ρ(m) = 2 πλ √ λ− m2 , − √ λ ≤ m ≤ √ λ. (2.14) The spectral density is n”
Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings (2007, neutral): “Contents”
Random matrices. (2015, background): “(The relation between random matrix theory and string theory had been noticed earlier by Dijkgraaf and Vafa [16].”
Gravity Induced C-Deformation (2003, background): “ar X iv :h ep -t h/ 03 03 06 3v 1 7 M ar 2 00 3 CALT-68-2433 HUTP-03/A020 hep-th/0303063 Gravity Induced C-Deformation Hirosi Ooguri1 and Cumrun Vafa1,2 1 California Institute of Technology 452-48, Pasadena, CA 91125, USA 2 Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, USA ”
A Perturbative Window into Non-Perturbative Physics (2002, methodology): “Note that we have isolated a rare phenomenon, a gauge theory quantity for which the planar limit is exact! As we showed in [18], in this specific example of a single adjoint chiral matter field one can solve for the exact large N result directly using standard random matrices techniques.”