Five-dimensional Chern-Simons terms and Nekrasov's instanton counting

TL;DR

This paper extends Nekrasov's five-dimensional super Yang-Mills prepotential by including Chern-Simons terms, enabling the calculation of topological string partition functions on toric Calabi-Yau manifolds.

Contribution

It introduces a gauge theory approach to incorporate Chern-Simons effects into Nekrasov's framework, matching topological string results for all relevant cases.

Findings

Reproduces topological A-model partition functions for all m=0,...,N

Extends Nekrasov's prepotential to include Chern-Simons terms

Provides a gauge theory derivation for geometric engineering results

Abstract

We extend the graviphoton-corrected prepotential of five-dimensional pure U(N) super Yang-Mills, which was originally proposed by Nekrasov, by incorporating the effect of the five-dimensional Chern-Simons term. This extension allows us to reproduce by a gauge theory calculation the partition functions of corresponding topological A-model on local toric Calabi-Yau manifolds X^m_N for all m=0,1,...,N. The original proposal corresponds to the case m=0.