On K3-Thurston 7-manifolds and their deformation space: A case study with remarks on general K3T and M-theory compactification

TL;DR

This paper constructs and analyzes a special class of 7-manifolds called K3-Thurston (K3T), exploring their deformation spaces with structures relevant to M-theory compactifications and supersymmetric gauge theories.

Contribution

It introduces K3T 7-manifolds with specific deformation space structures, linking geometric properties to M-theory and supersymmetry.

Findings

Deformation space from K3 part admits a Kähler structure.

Thurston part of the deformation space admits a special Kähler structure.

Remarks on generalizations and M-theory interfaces.

Abstract

M-theory suggests the study of 11-dimensional space-times compactified on some 7-manifolds. From its intimate relation to superstrings, one possible class of such 7-manifolds are those that have Calabi-Yau threefolds as boundary. In this article, we construct a special class of such 7-manifolds, named as {\it K3-Thurston} (K3T) 7-manifolds. The factor from the K3 part of the deformation space of these K3T 7-manifolds admits a K\"{a}hler structure, while the factor of the deformation space from the Thurston part admits a special K\"{a}hler structure. The latter rings with the nature of the scalar manifold of a vector multiplet in an N=2 $d=4$ supersymmetric gauge theory. Remarks and examples on more general K3T 7-manifolds and issues to possible interfaces of K3T to M-theory are also discussed.