Effect of Zero Modes on the Bound-State Spectrum in Light-Cone Quantisation

TL;DR

This paper investigates how bosonic zero modes influence the bound-state spectrum in light-cone quantisation of 2D SU(2) Yang-Mills theory, revealing that including dynamical zero modes causes significant mass shifts.

Contribution

It demonstrates the importance of dynamical zero modes in light-cone quantisation and quantifies their impact on the bound-state mass spectrum in a simplified gauge theory.

Findings

Dynamical zero modes mix with the Fock vacuum.

Omission of constrained modes results in an infinite square-well potential.

Including zero modes causes approximately 21% mass shifts in lowest states.

Abstract

We study the role of bosonic zero modes in light-cone quantisation on the invariant mass spectrum for the simplified setting of two-dimensional SU(2) Yang-Mills theory coupled to massive scalar adjoint matter. Specifically, we use discretised light-cone quantisation where the momentum modes become discrete. Two types of zero momentum mode appear -- constrained and dynamical zero modes. In fact only the latter type of modes turn out to mix with the Fock vacuum. Omission of the constrained modes leads to the dynamical zero modes being controlled by an infinite square-well potential. We find that taking into account the wavefunctions for these modes in the computation of the full bound state spectrum of the two dimensional theory leads to 21% shifts in the masses of the lowest lying states.