Abelian matrix models in two loops Original Research Article

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 Ai endowed with a non-trivial conformally flat metric gij=δij1+12|A|3−34|A|6+⋯. For the matrix model obtained from Abelian 4D, N=2 theory, the two-loop correction ∝1/|A|6 vanishes as it should.