I'd like to understand the equivalence of orbifold theories in string theory and (2D worldsheet) QFTs with finite gauge group, using the path integral.
Suppose my action is S=12πα′∫d2σ(∂iXμ∂iXμ)
and the Xμ(σ) are invariant under some finite group action Γ. To construct the orbifold theory on a Riemann surface Σ, I want to take the path integral over the untwisted and twisted sectors, i.e. I want to average over all boundary conditions on Xμ in which Xμ is periodic up to Γ-action.
Now, on the other hand, if I want to compute the path integral of a QFT with a finite gauge group, I would "gauge-fix" and then compute the path integral.
How can I see that the two approaches are the same?
This post imported from StackExchange Physics at 2019-09-16 20:25 (UTC), posted by SE-user Dwagg