On Asymptotic Hamiltonian for SU(N) Matrix Theory

TL;DR

This paper calculates the leading effective Hamiltonian for SU(N) matrix theory at large separation, revealing a free Hamiltonian along flat directions, with implications for ground states and Witten index corrections.

Contribution

It extends the generalized Born-Oppenheimer approximation to SU(N) matrix theory, providing new insights into the effective Hamiltonian structure.

Findings

Effective Hamiltonian is free along flat directions.

Extension of Born-Oppenheimer approximation to SU(N).

Discussion on ground state candidates and Witten index correction.

Abstract

We compute the leading contribution to the effective Hamiltonian of SU(N) matrix theory in the limit of large separation. We work with a gauge fixed Hamiltonian and use generalized Born-Oppenheimer approximation, extending the recent work of Halpern and Schwartz for SU(2). The answer turns out to be a free Hamiltonian for the coordinates along the flat directions of the potential. Applications to finding ground state candidates and calculation of the correction (surface) term to Witten index are discussed.