
We study the orientifold truncation that arises when compactifying type II string theory on Calabi-Yau orientifolds with O3/O7-planes, in the context of supergravity. We look at the N=2 to N=1 reduction of the hypermultiplet sector of N=2 supergravity under the truncation, for the case of very special quaternionic-Kaehler target space geometry. We explicitly verify the Kaehler structure of the truncated spaces, and we study the truncated isometry algebra. For symmetric special quaternionic spaces, we give a complete overview of the spaces one finds after truncation. We also find new examples of dual Kaehler spaces, that give rise to flat potentials in N=1 supergravity.
25 pages, LaTeX, v2:curvature tensor of the dual symmetric spaces calculated, section 7 expanded, references added, v3:few typos fixed, version to appear in Class.Quantum Gravity
High Energy Physics - Theory, minimal coupling., FOS: Physical sciences, reduction, String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Calabi-Yau manifolds (algebro-geometric aspects), Supergravity, orientifold, Hyper-Kähler and quaternionic Kähler geometry, ``special'' geometry, potentials, quaternionic-Kähler geometry, High Energy Physics - Theory (hep-th), isometry algebra, Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis, Kaluza-Klein and other higher-dimensional theories, Calabi-Yau theory (complex-analytic aspects)
High Energy Physics - Theory, minimal coupling., FOS: Physical sciences, reduction, String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Calabi-Yau manifolds (algebro-geometric aspects), Supergravity, orientifold, Hyper-Kähler and quaternionic Kähler geometry, ``special'' geometry, potentials, quaternionic-Kähler geometry, High Energy Physics - Theory (hep-th), isometry algebra, Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis, Kaluza-Klein and other higher-dimensional theories, Calabi-Yau theory (complex-analytic aspects)
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