The Light-Cone Vacuum in 1+1 Dimensional Super-Yang-Mills Theory

TL;DR

This paper investigates the vacuum structure of 1+1 dimensional super-Yang-Mills theory using Discrete Light-Cone Quantization, revealing that zero modes are essential for understanding supersymmetry and phase properties of the vacuum.

Contribution

It provides a tractable analysis of zero modes in supersymmetric light-cone quantization, showing their role in vacuum degeneracy and supersymmetry preservation.

Findings

Ground state energy is zero and N-fold degenerate.

Zero modes are crucial for probing vacuum phases.

Supersymmetry algebra remains unchanged with zero modes.

Abstract

The Discrete Light-Cone Quantization (DLCQ) of a supersymmetric SU(N) gauge theory in 1+1 dimensions is discussed, with particular emphasis given to the inclusion of all dynamical zero modes. Interestingly, the notorious `zero-mode problem' is now tractable because of special supersymmetric cancellations. In particular, we show that anomalous zero-mode contributions to the currents are absent, in contrast to what is observed in the non-supersymmetric case. We find that the supersymmetric partner of the gauge zero mode is the diagonal component of the fermion zero mode. An analysis of the vacuum structure is provided and it is shown that the inclusion of zero modes is crucial for probing the phase properties of the vacua. In particular, we find that the ground state energy is zero and N-fold degenerate, and thus consistent with unbroken supersymmetry. We also show that the inclusion of zero modes for the light-cone supercharges leaves the supersymmetry algebra unchanged. Finally, we remark that the dependence of the light-cone Fock vacuum in terms of the gauge zero is unchanged in the presence of matter fields.