  Worldsheet string theory compactified on exceptional holomony manifolds is
revisited following arXiv:1809.06376, where aspects of the chiral symmetry were
described for the case where the compact space is a 7-dimensional
G$_2$-holonomy manifold constructed as a Twisted Connected Sum. We reinterpret
this result and extend it to Extra Twisted Connected Sum G$_2$-manifolds, and
to 8-dimensional Generalized Connected Sum Spin(7)-manifolds. Automorphisms of
the latter construction lead us to conjecture new mirror maps.
