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.
Highlights
In this work we extend upon [1], where general symmetry aspects of the σ-model in a generic TCS manifold were first investigated
We have shown that this geometric structure is encoded in the diamond of chiral algebras, see figure 5(b), so a mirror map respecting the Generalized Connected Sum” (GCS) structure has to correspond to an automorphism of the top algebra Od3 ⊕ Fr2 preserving the diamond
In this paper we have explored the relationship between the geometry of connected sum manifolds M of holonomies G2 and Spin(7), and the chiral algebra of the associated σ-model
Summary
We set up notations and the dictionary between target space and worldsheet symmetries which will be useful throughout the rest of the paper. More generally this correspondence yields a uniform and satisfying interpretation of the chiral algebras we will need in this paper. They are listed, where we provide the relevant holonomy groups G, covariantly constant tensors, and our notations for the corresponding worldsheet currents. The reverse inclusion, unadressed in [1], is perhaps even more interesting, because it informs on worldsheet symmetries of TCS G2-manifolds, which could conceivably be larger than those of a generic G2-manifold.
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