I'm currently reading the Seiberg-Witten paper on $N=2$ supersymmetric Yang Mills pure gauge theory (i.e. no hypermultiplets). I have the following question:
How does one understand that the metric on the moduli space of the full quantum theory is the same as the metric obtained from the Kahler potential for the scalar field (or in general the $N=1$ chiral superfield) in the low-energy effective theory? On the face of it, the two things seem quite different - while the moduli space is the space of all gauge-inequivalent vacua in the full theory, the Kahler metric is derived from the Kahler potential in the low energy theory.