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

Superconformal algebras for generalized Spin(7) and G$_2$ connected sums