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

TL;DR

This paper explores the algebraic structures of superconformal algebras in string theory compactifications on special holonomy manifolds, extending previous work to new geometric constructions and proposing potential mirror symmetries.

Contribution

It extends the understanding of superconformal algebras to generalized Spin(7) and G$_2$ connected sum manifolds, introducing new conjectures on mirror maps.

Findings

Extended chiral symmetry descriptions to new G$_2$-manifold constructions.

Reinterpreted previous results in the context of generalized connected sums.

Proposed new mirror symmetry conjectures based on automorphisms.

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.