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By now, a lot is known about orbifolds of 1+1-dimensional CFTs. Consider starting out with an arbitrary 'seed' CFT, $\mathcal{C}$, and take $N$ copies, $\mathcal{C}^{\otimes N}$ and then quotient by a permutation group $\Omega_N$.

$$\mathcal{C}^{\otimes N}/\Omega_N$$

It is known that performing this operation reorganizes the spectrum of the seed CFT, $\mathcal{C}$. In particular, there is the untwisted sector which projects only on to the $\Omega_N$-invariant states and there are additional twisted sectors to have modular invariance.

The above action on $\mathcal{C}$ looks fairly geometrical and seems to be rather generic if we had replaced the CFT by a non-conformal QFT.

Can one consider orbifolds of the above kind for non-conformal (1+1)-dimensional QFTs? Or are there any obstructions?
For sure, we would lack the technology of twist operators, their OPEs and the benefits of conformal invariance. Nevertheless, will the spectrum of the 'seed' QFT get reshuffled in the same manner as it happens for CFTs?

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