On relation between Nekrasov functions and BS periods in pure SU(N) case

Details On relation between Nekrasov functions and BS periods in pure SU(N) case On relation between Nekrasov functions and BS periods in pure SU(N) case

2010-01-11

arxiv.org/abs/1001.1407v1

Physics

High Energy Physics

High Energy Physics - Theory

12 pages

Scientific paper

We investigate the duality between the Nekrasov function and the quantized Seiberg-Witten prepotential, first guessed in [1] and further elaborated in [2] and [3]. We concentrate on providing more thorough checks than the ones presented in [3] and do not discuss the motivation and historical context of this duality. The check of the conjecture up to $o (\hbar^6, \ln (\Lambda))$ is done by hands for arbitrary $N$ (explicit formulas are presented). Moreover, details of the calculation that are essential for the computerization of the check are worked out. This allows us to test the conjecture up to $\hbar^6$ and up to higher powers of $\Lambda$ for $N = 2,3,4$. Only the case of pure SU(N) gauge theory is considered.

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