Lectures on Instanton Counting

الأصل · EN

These notes have two parts. The first is a study of Nekrasov's deformed partition functions Z(₁,₂,a;,τ) 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 R⁴. 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,a;,0). We put higher Casimir operators to the partition function and clarify their relation to the Seiberg-Witten u-plane. We also determine the coefficients of ₁₂ and (₁²+₂²)/3 (the genus 1 part) of the partition function, which coincide with two measure factors A, B appeared in the u-plane integral. The proof is based on the blowup equation which we derived in the previous paper.