Type-II Calabi-Yau compactifications, T-duality and special geometry in general spacetime signature

Abstract

We obtain the bosonic Lagrangians of vector and hypermultiplets coupled to four-dimensional $\mathcal{N}=2$ supergravity in signatures $(0,4)$, $(1,3)$ and (2,2) by compactification of type-II string theories in signatures (0,10), (1,9) and (2,8) on a Calabi-Yau threefold. Depending on the signature and the distinctions between type-IIA/IIA${}^{\ast }$/IIB/IIB${}^{\ast }$/IIB' the resulting scalar geometries are special Kähler or special para-Kähler for vector multiplets and quaternion-Kähler or para-quaternion Kähler for hypermultiplets. By spacelike and timelike reductions we obtain three-dimensional $\mathcal{N}=4$ supergravity theories coupled to two sets of hypermultiplets. We determine the c-maps relating vector to hypermultiplets, and show how the four-dimensional theories are related by spacelike, timelike and mixed, signature-changing T-dualities.

42 pages (including 10 page appendix), 14 tables, 2 figures. v2: LaTeX problem with arXiv identifiers fixed

References in corpus (5)

• Special Geometry of Euclidean Supersymmetry III: the local r-map, instantons and black holes
• Allowable complex metrics in minisuperspace quantum cosmology
• Special Geometry and Space-time Signature
• Euclidean Actions, Instantons, Solitons and Supersymmetry
• Supersymmetry algebras in arbitrary signature and their R-symmetry groups

Cited by in corpus (1)

• Note on complex metrics, complex time and periodic universes