Usually we say there are two types of heterotic strings, namely $E_8\times E_8$ and $Spin(32)/\mathbb{Z}_2$. (Let's forget about nonsupersymmetric heterotic strings for now.)
The standard argument goes as follows.

To have a supersymmetric heterotic string theory in 10d, you need to use a chiral CFT with central charge 16, such that its character $Z$ satisfies two conditions:
 $Z(1/\tau)=Z(\tau)$
 $Z(\tau+1)=\exp(2\pi i/3) Z(\tau)$

Such a chiral CFT, if we use the lattice construction, needs an even selfdual lattice of rank 16.
 There are only two such lattices, corresponding to the two already mentioned above.
We can replace the lattice construction with free fermion construction, and we still get the same result. But mathematically speaking, there might still be a chiral CFT of central charge 16, with the correct property, right? Is it studied anywhere?
This post has been migrated from (A51.SE)