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

Abstract

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.

Reference added, minor changes in sections 3 and 4 to match published version. 34 pages