Instanton Counting and Chern-Simons Theory

By Amer Iqbal, A. Kashani-Poor. 2002

158 citations recorded by the source corpus.

The instanton partition function of N = 2, D = 4 SU(2) gauge theory is obtained by taking the field theory limit of the topological open string partition function, given by a Chern-Simons theory, of a CY3-fold. The CY3-fold on the open string side is obtained by geometric transition from local IP{sup 1} x IP{sup 1} which is used in the geometric engineering of the SU(2) theory. The partition function obtained from the Chern-Simons theory agrees with the closed topological string partition function of local IP{sup 1} x IP{sup 1} proposed recently by Nekrasov. We also obtain the partition functions for local F{sub 1} and F{sub 2} CY3-folds and show that the topological string amplitudes of all three local Hirzebruch surfaces give rise to the same field theory limit. It is shown that a generalization of the topological closed string partition function whose field theory limit is the generalization of the instanton partition function, proposed by Nekrasov, can be determined easily from the Chern-Simons theory.

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

View Paper: https://www.semanticscholar.org/paper/8be180145bc55fcd4cc65ccea508d1269479965f

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. C. Vafa
3. A. Klemm
4. Mina Aganagic
5. Masato Taki
6. Sara Pasquetti
7. C. Kozçaz
8. R. Dijkgraaf

In Nuclear and High Energy Physics

1. Marcos Mariño
2. C. Vafa
3. A. Klemm
4. Mina Aganagic
5. R. Dijkgraaf
6. Sara Pasquetti
7. Masato Taki
8. Amer Iqbal

In Statistical and Nonlinear Physics

1. Marcos Mariño
2. C. Vafa
3. A. Klemm
4. Mina Aganagic
5. Sara Pasquetti
6. Masato Taki
7. C. Kozçaz
8. V. Bouchard

Citations in the corpus

• Matrix models, geometric engineering and elliptic genera (2003, methodology): “The instanton partition function given above although looks different but is exactly the equal to the one calculated in the last section (for the case of U(1) and U(2)) if we use the following two identities [64], ∞ ∏”
• Remodeling the B-Model (2007, background): “There is also another interesting phase in the local F1 moduli space — see for instance [36].”
• 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.”
• The refined topological vertex (2007, background): “As we saw in [6], the partition function for local Fm differ just by framing factors along the edges which label the instanton charge (the edges corresponding to the base P(1)).”
• Quantum geometry of refined topological strings (2011, background): “In fact, it was explicitly verified in [31, 32] that in the special case (3.”
• Black Holes, q-Deformed 2d Yang-Mills, and Non-perturbative Topological Strings (2004, background): “7) As follows from [25] the functions KRS and NRS are expressed in terms of fRS(q) as KRS(Q, q) = K.”
• 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].”
• Refined Topological Vertex and Instanton Counting (2007, methodology): “The partition function of the A-model on the toric Calabi-Yau agrees with the Nekrasov’s partition function of N= 2 SU(N) gauge theory [7][8][9][10][11][12][13].”
• Chern-Simons theory and topological strings (2004, methodology): “prepotential. This was explicitly verified by Iqbal and Kashani-Poor (2003a) by using the expression (7.41) and the results of Nekrasov (2002) for the Seiberg-Witten prepotential.”
• The Topological Vertex (2003, methodology): “In this setup we identify the B-branes on the mirror Riemann surface as fermions related to the chiral boson by bosonization.”