Nekrasov prepotential with fundamental matter from the quantum spin chain

Nekrasov functions were conjectured in \cite{Mironov:2009uv} to be related to exact Bohr-Sommerfeld periods of quantum integrable systems. This statement was thoroughly checked for the case of the pure $SU(N_c)$ gauge theory in \cite{Mironov:2009dv} and \cite{Popolitov:2010bz}. Here we successfully perform a set of checks in the case of gauge group $SU(N_c)$ with additional $N_f$ fundamental hypermultiplets. We show that the Baxter equation for the spin chain gives the same quantum periods as the one for the Gaudin system in this case.

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