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*/IIB/IIB*/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.
Highlights
String theory is a web of perturbatively defined theories which are related to each other by various dualities
In this paper we will obtain the bosonic actions for four-dimensional N = 2 supergravity coupled to vector and hypermultiplets in signatures (0, 4), (1, 3) and (2, 2) by compactification of type-II string theories in signatures (0, 10), (1, 9), (2, 8) on Calabi-Yaur threefolds
According to [30, 31], there is a correspondence between the planar cosmological solutions in N = 2 vector multiplet theories that can be embedded into type-II string theory, and planar black hole solutions in vector multiplet theories realizing the twisted N = 2 supersymmetry algebra, which, as we show in this paper, can be embedded into type-II∗
Summary
String theory is a web of perturbatively defined theories which are related to each other by various dualities. In this paper we will obtain the bosonic actions for four-dimensional N = 2 supergravity coupled to vector and hypermultiplets in signatures (0, 4), (1, 3) and (2, 2) by compactification of type-II string theories in signatures (0, 10), (1, 9), (2, 8) on Calabi-Yaur threefolds Carrying out these reductions is straightforward since for type-IIA one can adapt the computations of [16, 18], while the corresponding results for type-IIB are fixed by mirror symmetry. According to [30, 31], there is a correspondence between the planar cosmological solutions in N = 2 vector multiplet theories that can be embedded into type-II string theory, and planar black hole solutions in vector multiplet theories realizing the twisted N = 2 supersymmetry algebra, which, as we show in this paper, can be embedded into type-II∗ Both solutions can be related to the same four-dimensional Euclidean partition function, which explains that their Killing horizons satisfy the same thermodynamic relations [31].
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