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Instanton counting, Macdonald function and the moduli space of D-branes

Hidetoshi Awata·Hiroaki Kanno
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Abstract

We argue the connection of Nekrasov's partition function in the Ωbackground and the moduli space of D-branes, suggested by the idea of geometric engineering and Gopakumar-Vafa invariants. In the instanton expansion of N=2 SU(2) Yang-Mills theory the Nakrasov's partition function with equivariant parameters ε_1, ε_2 of toric action on C^2 factorizes correctly as the character of SU(2)_L \times SU(2)_R spin representation. We show that up to two instantons the spin contents are consistent with the Lefschetz action on the moduli space of D2-branes on (local) F_0. We also present an attempt at constructing a refined topological vertex in terms of the Macdonald function. The refined topological vertex with two parameters of T^2 action allows us to obtain the generating functions of equivariant χ_y and elliptic genera of the Hilbert scheme of n points on C^2 by the method of topological vertex.

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Hidetoshi Awata, Hiroaki Kanno. 2005-04-08. Instanton counting, Macdonald function and the moduli space of D-branes. https://doi.org/10.1088/1126-6708%2F2005%2F05%2F039

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