Possible Mechanism for Vacuum Degeneracy in YM2 in DLCQ

Abstract

SU(2) Yang-Mills Theory coupled to massive adjoint scalar matter is studied in (1+1) dimensions using Discretised Light-Cone Quantisation. The gauge fixing and quantisation of the theory is briefly discussed. The most difficult problem is the presence of a constrained zero mode of a matter field component, analogous to structures which in other theories have given rise to the correct vacuum structure in those contexts. Here the novelty is the coupling of this problem with a dynamical zero mode coming from the gluon part of the theory. I develop a diagrammatic method to solve the constraint equation. The implementation of the solution in the potential governing the vacuum dynamics of the independent zero mode leads to a centrifugal barrier. This double well structure seems consistent with the two-fold vacuum degeneracy to be expected from a standard ‘instanton’ analysis. However, the barrier height seems too low still to bring states into approximate degeneracy. It is suggested that an improper treatment of the renormalisation is the cause of this.