Born – Oppenheimer corrections to the effective zero - mode Hamiltonian in SYM theory

We calculate the subleading terms in the Born–Oppenheimer expansion for the effective zero-mode Hamiltonian of N = 1, d = 4 supersymmetric Yang–Mills theory with any gauge group. The Hamiltonian depends on 3r abelian gauge potentials Ak (k = 1, 2, 3, s = 1, . . . , r, r is the rank of the group), and their superpartners. The Hamiltonian belongs to the class ofN = 2 supersymmetric QM Hamiltonian constructed earlier by Ivanov and I. Its bosonic part describes the motion over the 3r–dimensional manifold with a special metric. The corrections explode when the root forms αj(A s k) vanish and the Born–Oppenheimer approximation breaks down.