Instanton counting on blowup. I. 4-dimensional pure gauge theory

By H. Nakajima, K. Yoshioka. 2003

361 citations recorded by the source corpus.

We give a mathematically rigorous proof of Nekrasov’s conjecture: the integration in the equivariant cohomology over the moduli spaces of instantons on ℝ4 gives a deformation of the Seiberg-Witten prepotential for N=2 SUSY Yang-Mills theory. Through a study of moduli spaces on the blowup of ℝ4, we derive a differential equation for the Nekrasov’s partition function. It is a deformation of the equation for the Seiberg-Witten prepotential, found by Losev et al., and further studied by Gorsky et al.

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

View Paper: https://www.semanticscholar.org/paper/6611236363fd9cdc2fd915b6cdaa72d2750ee699

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In Nuclear and High Energy Physics

1. C. Vafa
2. A. Klemm
3. Masato Taki
4. Marcos Mariño
5. Min-xin Huang
6. Amer Iqbal
7. C. Kozçaz
8. A. Hanany

In Statistical and Nonlinear Physics

1. C. Vafa
2. A. Klemm
3. Masato Taki
4. Marcos Mariño
5. Min-xin Huang
6. C. Kozçaz
7. Amer Iqbal
8. A. Hanany

Citations in the corpus

• The Ω Deformed B-model for Rigid N = 2 Theories (2011, background): “This expression appeared first as an equivariant instanton partition function of N = 2 SU(N) gauge theories in [3, 4] and was generalized to arbitrary gauge groups in [5, 6].”
• The refined topological vertex (2007, methodology): “used to calculate the gauge theory partition function has more refined information. Recall that on the gauge theory side the partition function is calculated using localization in equivariant K-theory [10,11] with respect to an r+ 2 dimensional torus T2 ×K, where K is the r dimensional maximal torus ”
• Instanton counting on blowup. II. K-theoretic partition function (2005, methodology): “...,e r. In our previous paper [ 13 ], these are generators of the equivariant cohomology group H ∗”
• The elliptic Hall algebra and the equivariant K-theory of the Hilbert scheme of $\mathbb{A}^2$ (2009, neutral): “ (λ(1),λ(2),...λ(r)) corresponds a fixed point I λ such that the class Tλ= [TI λ Mr,n] in Ris given by (8.4) Tλ= Xr α,β=1 χ−1 β χα X s∈λ(α ) tl λ(β)(s)q−a (α)(s)−1 + X β t−l (α)(s)−1qa (β)(s) , see [21], Theorem 2.11. 8.3. The tautological bundle of Mr,nis the T-equivariant locally free sheaf τngive”
• Counting gauge invariants: The Plethystic program (2007, background): “In fact, in this case, [38] has given, in our notation, the ν-inserted plethystic exponential (cf.”
• Refined Topological Vertex and Instanton Counting (2007, methodology): “His conjectual observation was mathematically verified by Nekrasov-Okounkov [23], Nakajima-Yoshioka [24], and Braverman [25].”