  In this work we study the Nekrasov-Shatashvili limit of the Nekrasov
instanton partition function of Yang-Mills field theories with N=2
supersymmetry and gauge group SU(n). The theories are coupled with fundamental
matter. The equation that determines the density of eigenvalues at the leading
order in the saddle-point approximation is exactly solved. The dominating
contribution to the instanton free energy is computed. The requirement that
this energy is finite imposes quantization conditions on the parameters of the
theory that are in agreement with analogous conditions that have been derived
in previous works. Using methods borrowed from the theory of matrix models, a
field theoretical expression of the full instanton partition function is
derived. It is checked that in the Nekrasov-Shatashvili (thermodynamic) limit
the action of the field theory obtained in this way reproduces exactly the
equation of motion used in the saddle-point calculations.
