SU(N) Geometries and Topological String Amplitudes

By Amer Iqbal, A. Kashani-Poor. 2003

170 citations recorded by the source corpus.

It has been conjectured recently that the field theory limit of the topological string partition functions, including all higher genus contributions, for the family of CY3folds giving rise to N = 2 4D SU(N) gauge theory via geometric engineering can be obtained from gauge instanton calculus. We verify this surprising conjecture by calculating the partition functions for such local CYs using diagrammatic techniques inspired by geometric transitions. Determining the Gopakumar-Vafa invariants for these geometries to all orders in the fiber wrappings allows us to take the field theory limit.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/17fca81a53b8ba157a409118f2928b17a2e81476

How researchers see this paper

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

In Astronomy and Astrophysics

1. Marcos Mariño
2. A. Klemm
3. C. Vafa
4. Mina Aganagic
5. R. Dijkgraaf
6. T. Hollowood
7. Amer Iqbal
8. H. Kanno

In Nuclear and High Energy Physics

1. Marcos Mariño
2. C. Vafa
3. A. Klemm
4. Mina Aganagic
5. Amer Iqbal
6. R. Dijkgraaf
7. H. Kanno
8. H. Awata

In Statistical and Nonlinear Physics

1. Marcos Mariño
2. C. Vafa
3. A. Klemm
4. Mina Aganagic
5. R. Dijkgraaf
6. Amer Iqbal
7. A. Okounkov
8. Tohru Eguchi

Citations in the corpus

• The refined topological vertex (2007, unknown): “= q ||ν1|| (2)+||ν2|| (2)+||ν3|| 2 2 Z̃ν1(t, q)Z̃ν2(t, q)Z̃ν3(t, q) ∏ i,j(1−Q1tj−1/2−ν t 1,iqi−1/2−ν2,j )(1−Q2t t 2,iqi−1/2−ν3,j )(1−Q1Q2t t 1,iqi−1/2−ν3,j ) In the above expression −log(Q1) and −log(Q2) are the Kähler classes of the P(1)’s in the fiber and Qb1,b2,b3 are given by [7] Qb1 = QbQ m+1 1”
• Instanton counting, Macdonald function and the moduli space of D-branes (2005, background): “The first example was given by the geometric transition based on the duality of the resolved conifold and the deformed conifold [1][2].”
• Matrix models, geometric engineering and elliptic genera (2003, methodology): “The link between the topological string computations and the 5d gauge theory computation of Nekrasov has been proven in [64,63].”
• Quantum Calabi-Yau and Classical Crystals (2003, background): “This is an interesting class to study, as it leads to nontrivial predictions for instanton corrections to gauge and gravitational couplings of a large class of N = 2 supersymmetric gauge theories in four dimensions via geometric engineering [4] (for recent progress in this direction see [5, 6]).”
• Topological Strings and Integrable Hierarchies (2003, background): “Example 4: Integrable structure of the topological vertex The topological vertex was introduced in [9] as the building block for topological string amplitudes on local, toric Calabi-Yau threefolds (for further properties and applications of the topological vertex, see for example [44,45,46,47,48,49]”
• A& B model approaches to surface operators and Toda thoeries (2010, unknown): “20 25 v2 [ he p- th ] 1 5 A pr 2 01 Table of contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2”
• Quantum geometry of refined topological strings (2011, background): “In fact, it was explicitly verified in [31, 32] that in the special case (3.”
• Topological strings and Nekrasov's formulas (2003, result): “We find an exact agreement of the results of our computation with the formula proposed recently by Nekrasov for N = 2 SU(2) gauge theory with two parameters β and ~. β is related to the size of the fiber of F0 and ~ corresponds to the string coupling constant.”
• REFINED BPS STATE COUNTING FROM NEKRASOV'S FORMULA AND MACDONALD FUNCTIONS (2008, background): “3 Geometric engineering and toric geometry In this section following [4, 5, 8, 11], we review the toric geometry that is necessary for geometric engineering.”