  We perform a two-loop calculation of the effective Lagrangian for the
low--energy modes of the quantum mechanical system obtained by dimensional
reduction from 4D, N = 1 supersymmetric QED. The bosonic part of the Lagrangian
describes the motion over moduli space of vector potentials A_i endowed with a
nontrivial conformally flat metric. We determined the coefficient of the
two-loop correction to the metric, which is proportional to 1/A^6. For the
matrix model obtained from Abelian 4D, N = 2 theory, this correction vanishes,
as it should.
