Does fixing the reparameterisation invariance of the string action, for example by choosing the light-cone gauge correspond to some kind of orbifolding? This answer explains that gauge systems are orbifolds after removing the gauge redundancy. So, as the reparameterization invariance of the string action is nothing else but the worldsheet diffeomorphism invariance which is a gauge symmetry, does fixing it by the light-cone gauge correspond to some kind of orbifolding too? If this way of thinking is wrong, I would highly appreciate any clarifications of what I am confusing.