Topological strings and Nekrasov's formulas

By Tohru Eguchi, H. Kanno. 2003

143 citations recorded by the source corpus.

We apply the method of geometric transition and compute all genus topological closed string amplitudes compactified on local F0 by making use of the Chern-Simons gauge theory. We find an exact agreement of the results of our computation with the formula proposed recently by Nekrasov for = 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. Thus Nekrasov's formula encodes all the information of topological string amplitudes on local F0 including the number of holomorphic curves at arbitrary genus. By taking suitable limits β and/or →0 one recovers the four-dimensional Seiberg-Witten theory and also its coupling to external graviphoton fields. We also compute topological string amplitude for the local 2nd del Pezzo surface and check the consistency with Nekrasov's formula of SU(2) gauge theory with a matter field in the vector representation.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/24a4d14e6d3f6945e94b5ad7b03d3b71414480cd

How researchers see this paper

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

In Atomic and Molecular Physics, and Optics

1. Marcos Mariño
2. Masato Taki
3. H. Nakajima
4. K. Yoshioka
5. Sara Pasquetti
6. H. Awata
7. C. Vafa
8. Amer Iqbal

In Nuclear and High Energy Physics

1. C. Vafa
2. Marcos Mariño
3. A. Klemm
4. Mina Aganagic
5. Masato Taki
6. Amer Iqbal
7. H. Kanno
8. C. Kozçaz

Citations in the corpus

• 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, background): “It is well known that the A-model topological string partition function for the toric Calabi-Yau which engineers a certain N = 2 quiver gauge theory is equal to the Nekrasov instanton partition function for the corresponding (five-dimensional) gauge theory formulated on R4×S1 [9, 10].”
• REFINED BPS STATE COUNTING FROM NEKRASOV'S FORMULA AND MACDONALD FUNCTIONS (2008, background): “(1.2) The parameter Λ of instanton expansion is introduced as a dynamical scale in the renormalization.”
• Chern-Simons theory and topological strings (2004, unknown): “Further applications of the topological vertex to the computation of supersymmetric gauge theory amplitudes can be found in Iqbal and Kashani-Poor (2003b), Eguchi and Kanno (2003) and Hollowood, Iqbal, and Vafa (2003).”
• Lectures on instanton counting (2003, methodology): “the calculation by Morton-Lukac [56], Iqbal+Kashani-Poor show that the invariants of the Hopf link has the same combinatorial expression as that of F given by the localization formula [35]. (See also [19].) Note that these results identify the n-instanton correction with the GromovWitten invariants ”
• Matrix models, geometric engineering and elliptic genera (2003, background): “The case of Nf = 0, 1 was discussed recently in [68].”
• Refined Topological Vertex and Instanton Counting (2007, methodology): “In [10][9][11] the partition function was reproduced from the string calculation via the geometric engineering Z Nek.”
• 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].”