Superconformal algebras for generalized Spin(7) and G2 connected sums

Abstract

Worldsheet string theory compactified on exceptional holomony manifolds is revisited following [1], where aspects of the chiral symmetry were described for the case where the compact space is a 7-dimensional G2-holonomy manifold constructed as a Twisted Connected Sum. We reinterpret this result and extend it to Extra Twisted Connected Sum G2-manifolds, and to 8-dimensional Generalized Connected Sum Spin(7)-manifolds. Automorphisms of the latter construction lead us to conjecture new mirror maps.

Families of solutions of the heterotic G$_2$ system

“…It would be interesting to perform a worldsheet study of the solutions we have presented. This question has been addressed for G 2 twisted connected sums in [82], and for G 2 extra twisted connected sums as well as Spin(7) generalized connected sum manifolds in [83]. The AdS 3 spacetime factor would require the presence of the superconformal algebra introduced in [84].…”

Topological G2 and Spin(7) strings at 1-loop from double complexes

“…where [101]. 34 This equivalence of twisted bundle versus twisted derivative applies to all generalised tensor bundles and we will often move between the two pictures in (C.10) and will drop the superscript H to avoid cluttering our notation further. Since it geometrises the H flux, generalised geometry turns out to be naturally well suited to describe the NSNS sector of string backgrounds.…”

Topological G$_{2}$ and Spin(7) strings at 1-loop from double complexes

“…9 Though see, for example, [31][32][33][34] where T r defines a Virasoro algebra commuting with T I of central charge c = 23 2 . We can therefore label states as |∆ I , ∆ r with respect to their weights under T I and T r .…”

“…The equivalence of (C.7) and (C.8) comes from choosing a global isomorphism E H E. To do so, one must pick a connection B which is locally a 2-form, and patches as 33 [100]. 34 This equivalence of twisted bundle versus twisted derivative applies to all generalised tensor bundles and we will often move between the two pictures in (C.10) and will drop the superscript H to avoid cluttering our notation further. Since it geometrises the H flux, generalised geometry turns out to be naturally well suited to describe the NSNS sector of string backgrounds.…”

“…This non-trivial constraint on triple intersections means B is a connective structure on a gerbe[102] 34. In addition, this class must be quantised in string theory.…”