Non decoupling ghosts in the light cone gauge

TL;DR

This paper challenges the conventional ghost decoupling in light cone gauge, showing that using both light cone vectors instead of one allows for a consistent BRST formulation with non-decoupling ghosts.

Contribution

It demonstrates that employing both light cone vectors instead of one restores ghost presence and enables a consistent BRST framework in light cone gauge.

Findings

Ghosts do not decouple when both light cone vectors are used.

A consistent BRST theory can be constructed with non-decoupling ghosts.

The traditional decoupling is due to using only one light cone vector.

Abstract

The gist of using the light cone gauge lies in the well known property of ghosts decoupling. But from the BRST point of view this is a stringency since for the construction of a nilpotent operator (from a Lie algebra) the presence of ghosts are mandatory. We will show that this is a foible which has its origins in the very fact of using just one light cone vector ($n_\mu$) instead of working with both light cone vectors ($n_\mu$ and $m_\mu$) to fulfill the light cone base vectors. This will break out ghost decoupling from theory but allowing now a consistent BRST theory for the light cone gauge.