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

TL;DR

This paper rigorously tests the conjectured duality between Nekrasov functions and quantized Seiberg-Witten prepotentials for pure SU(N) gauge theories, providing explicit formulas and computational methods for higher-order checks.

Contribution

It offers detailed calculations and formulas to verify the duality conjecture up to high orders in  and  for arbitrary N, focusing on pure SU(N) theories.

Findings

Duality holds up to ^6 and higher powers of  for N=2,3,4

Explicit formulas enable computational verification of the conjecture

Work extends previous checks by providing detailed calculations and methods

Abstract

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.