# Does fixing the reparameterization invariance of the string action correspond to some kind of orbifolding?

Does fixing the reparameterization invariance of the string action, for example by choosing the light-cone gauge

$$X^{+} = \beta\alpha' p^{+}\tau$$

$$p^{+} = \frac{2\pi}{\beta} P^{\tau +}$$

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?

And if so, what are the characteristics of this orbifold, what singularities does it have, and is there some kind of double strike which projects certain states out of the theory and leads at the same time to the emergence new ones?

If this way of thinking is wrong, I would highly appreciate any clarifications of what I am confusing.

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without a specific math-oriented question, it is rather unlikely that you will receive a helpful response from this forum. –  Carlo Beenakker Oct 26 '13 at 20:19
@CarloBeenakker thanks for your concerns ... However, my hope is that as I have seen technical theoretical physics questions (such as about string-theory for example here, here, here, etc ... ) can find immensely nice answers on this site, that I will be lucky too. Even if it may take its time. –  Dilaton Oct 26 '13 at 22:53