Lectures on instanton counting
Nov, 2003Citations per year
Abstract:
These notes have two parts. The first is a study of Nekrasov's deformed partition functions Z(\ve_1,\ve_2,\vec{a}:\q,\vec{\tau}) of N=2 SUSY Yang-Mills theories, which are generating functions of the integration in the equivariant cohomology over the moduli spaces of instantons on . The second is review of geometry of the Seiberg-Witten curves and the geometric engineering of the gauge theory, which are physical backgrounds of Nekrasov's partition functions. The first part is continuation of math.AG/0306198, where we identified the Seiberg-Witten prepotential with Z(0,0,\vec{a}:\q,0). We put higher Casimir operators to the partition function and clarify their relation to the Seiberg-Witten -plane. We also determine the coefficients of \ve_1\ve_2 and (\ve_1^2+\ve_2^2)/3 (the genus 1 part) of the partition function, which coincide with two measure factors , appeared in the -plane integral. The proof is based on the blowup equation which we derived in the previous paper.Note:
- Dedicated to Professor Akihiro Tsuchiya on his sixtieth birthday
- lectures: Montreal 2003/07/14
- gauge field theory: Yang-Mills
- supersymmetry
- Seiberg-Witten model
- instanton
- moduli space
- Donaldson theory
- partition function
- potential: prepotential
- gravitation
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