On geometry and matrix models

By R. Dijkgraaf, C. Vafa. 2002

478 citations recorded by the source corpus.

Abstract We point out two extensions of the relation between matrix models, topological strings and N =1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large-N duals of the local Calabi–Yau geometries that engineer N =2 gauge theories. In particular, a double scaling limit of the Gross–Witten one-plaquette lattice model gives the SU(2) Seiberg–Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N =1 ADE quiver gauge theories is similarly computed by large-N multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/e730c0084c5173b4a5b170bb13c8e0ac86b3021a

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

1. Marcos Mariño
2. C. Vafa
3. Mina Aganagic
4. A. Klemm
5. R. Dijkgraaf
6. E. Witten
7. Amer Iqbal
8. Sh. Shakirov

In Nuclear and High Energy Physics

1. Marcos Mariño
2. C. Vafa
3. A. Klemm
4. Mina Aganagic
5. E. Witten
6. Y. Nakayama
7. R. Dijkgraaf
8. N. Seiberg

Citations in the corpus

• A Perturbative Window into Non-Perturbative Physics (2002, background): “In the previous example, and also in the case of the quiver matrix models considered in [19], this three-fold is of the special form”
• Les Houches lectures on matrix models and topological strings (2004, background): “6 Extensions and applications The results derived above can be extended to more complicated Calabi-Yau backgrounds with branes [28, 29].”
• Liouville Field Theory — A decade after the revolution (2004, methodology): “g [91, 122] for a recent discussion on the subject.”
• Chiral Rings and Phases of Supersymmetric Gauge Theories (2003, methodology): “A renaissance of this subject has recently been stimulated by the work of Dijkgraaf and Vafa [2], who, motivated by earlier developments [3-9], conjectured an interesting relation between SUSY gauge theories and matrix models.”
• Holomorphic anomaly in gauge theories and matrix models (2006, background): “Various holomorphic limits are readily taken from our expressions and provide conjectural solutions to the unitary matrix model [3].”
• Matrix model as a mirror of Chern-Simons theory (2002, unknown): “(3.5) Then, U = exp( 12gs ∫ IP1 ωTru2), where ω is a (1, 1) form on IP1 of unit volume.”
• Chern-Simons Theory, Matrix Integrals, and Perturbative Three-Manifold Invariants (2002, background): “Indeed, a compact version of this, corresponding to a unitary matrix model where the βi are periodic variables, has been considered in [17] in order to describe the stringy realization of the N = 2 Seiberg-Witten geometry.”
• Instanton Counting and Chern-Simons Theory (2002, background): “Large N dualities in the context of closed and open topological strings on different CY3fold backgrounds have been the source of much excitement recently [1, 2].”
• Perturbative analysis of gauged matrix models (2002, unknown): “It was shown in [1,2,3], building on previous work [4,5,6,7], that the planar diagrams of the matrix model effectively compute the exact glueball superpotential for the associated supersymmetric gauge theory and thus yield, upon extremization, exact results for the gauge theory.”
• Knot Homology from Refined Chern-Simons Theory (2011, methodology): “This matrix model generalizes the [49] and [50] matrix models to mirrors Y of toric geometries [27].”
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters (2015, background): “It appears that the exact computations of [24], [25] of effective superpotentials of N = 1 theories and their gravitational descendands can be cast in the form of the non-perturbative Dyson-Schwinger identities.”
• Matrix models, geometric engineering and elliptic genera (2003, methodology): “Following the logic of [21,66,67], we integrate out the fields Φ1(y, ȳ) and Φ2(y, ȳ) since they appear Gaussian in (2.”