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

TL;DR

This paper investigates the quantum states of instanton solitons in five-dimensional noncommutative U(N) Yang-Mills theories, revealing multiple ground states with D-string interpretations and analyzing their behavior under compactification.

Contribution

It derives the low energy dynamics of instanton solitons in noncommutative 5D theories and quantizes these to identify multiple ground states with specific properties.

Findings

Found N distinct ground states with unit Pontryagin number and no electric charge.

Established a D-string interpretation of the quantum states.

Demonstrated the stability of results under decompactification in the Coulomb phase.

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.