Quantum Spectrum of Instanton Solitons in Five Dimensional Noncommutative U(N) Theories

TL;DR

This work analyzes quantum states of instanton solitons (calorons) in five-dimensional noncommutative $U(N)$ Yang–Mills theories. By reducing to the low-energy dynamics on the smooth caloron moduli space and quantizing the resulting supersymmetric quantum mechanics, it is shown that in the Coulomb phase there are exactly $N$ bound states with unit Pontryagin number and no electric charge, supported by a D-string picture of monopole constituents. Decompactification to the Calabi metric preserves this bound-state count under suitable Higgs/Wilson-line conditions, highlighting the robustness of the result. Overall, the noncommutative regulator enables controlled analysis of instanton spectra in five dimensions and provides a clear link between caloron moduli spaces, monopole dynamics, and BPS bound states.

Abstract

We explore quantum states of instanton solitons in five dimensional noncommutative Yang-Mills theories. We start with maximally supersymmetric U(N) theory compactified on a circle S^1, and derive the low energy dynamics of instanton solitons, or calorons, which is no longer singular. Quantizing the low energy dynamics, we find N physically distinct ground states with a unit Pontryagin number and no electric charge. These states have a natural D-string interpretation. The conclusion remains unchanged as we decompactify S^1, as long as we stay in the Coulomb phase by turning on adjoint Higgs expectation values.