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

TL;DR

This paper computes subleading Born--Oppenheimer corrections to the effective zero-mode Hamiltonian in N=1, d=4 supersymmetric Yang--Mills theory, revealing breakdown points where the approximation fails.

Contribution

It provides the first calculation of these corrections for any gauge group, extending previous models of supersymmetric quantum mechanics.

Findings

Corrections depend on the gauge potentials in the Cartan subalgebra.

Breakdown of the approximation occurs when root forms vanish.

The Hamiltonian describes motion on a special 3r-dimensional manifold.

Abstract

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 A_i, lying in the Cartan subalgebra, and their superpartners (r being the rank of the group). The Hamiltonian belongs to the class of N = 2 supersymmetric QM Hamiltonia 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 \alpha_j(A_i) vanish and the Born--Oppenheimer approximation breaks down.