Planar Quantum Mechanics: an Intriguing Supersymmetric Example

TL;DR

This paper develops a Hamiltonian framework for planar quantum mechanics and explores a supersymmetric model, revealing a phase transition and a novel duality as functions of the coupling constant.

Contribution

It introduces a Hamiltonian formulation for planar quantum mechanics and demonstrates its effectiveness through a supersymmetric example with new duality insights.

Findings

Identifies a phase transition at coupling λ=1.

Discovers a strong-weak duality in the model.

Shows disappearance of the mass gap at the transition.

Abstract

After setting up a Hamiltonian formulation of planar (matrix) quantum mechanics, we illustrate its effectiveness in a non-trivial supersymmetric example. The numerical and analytical study of two sectors of the model, as a function of 't Hooft's coupling $\lambda$, reveals both a phase transition at $\lambda=1$ (disappearence of the mass gap and discontinuous jump in Witten's index) and a new form of strong-weak duality for $\lambda \to 1/\lambda$.