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arXiv 1209.0912hep-th
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N=2到N=1截断超引力中的亚稳de Sitter真空

Metastable de Sitter vacua in N=2 to N=1 truncated supergravity

Francesca Catino, Claudio A. Scrucca, Paul Smyth

摘要:

本文研究了在一般N=2到N=1截断超引力中不含矢量多重态时获得亚稳态de Sitter真空的可能性,并与N=2只含超多重态和N=1只含手征多重态的理论中的情形进行了比较.在基于四元数流形和引力光子规范的N=2理论中,德西特真空必然是不稳定的,这是由于几何的特殊性质。在基于卡勒流形和超势的N=1理论中,德西特真空可以是亚稳态的,只要几何满足某些约束,并且超势可以自由调整。在N=2到N=1的截断中,关键的要求是母理论的快子从子理论中投射出来,这样原来的不稳定真空就被投射到亚稳定真空中。我们研究的情况下,这可能会发生,并推导出一般的几何和测量亚稳性的限制。然后,我们详细研究了最简单的情况下,四元数流形的尺寸4至少有一个等距,存在一个一般的参数化,并研究两种类型的截断定义Kahler子流形的尺寸2。作为应用,我们最后讨论了N=2超弦的泛超多重态及其截断为N=1超弦的泛手征多重态的情形。我们认为,德西特真空在这样的理论是不稳定的弱耦合的情况下,而它们可以在原则上是亚稳定的强耦合制度。

英文摘要:

We study the possibility of achieving metastable de Sitter vacua in general N=2 to N=1 truncated supergravities without vector multiplets, and compare with the situations arising in N=2 theories with only hypermultiplets and N=1 theories with only chiral multiplets. In N=2 theories based on a quaternionic manifold and a graviphoton gauging, de Sitter vacua are necessarily unstable, as a result of the peculiar properties of the geometry. In N=1 theories based on a Kahler manifold and a superpotential, de Sitter vacua can instead be metastable provided the geometry satisfies some constraint and the superpotential can be freely adjusted. In N=2 to N=1 truncations, the crucial requirement is then that the tachyon of the mother theory be projected out from the daughter theory, so that the original unstable vacuum is projected to a metastable vacuum. We study the circumstances under which this may happen and derive general constraints for metastability on the geometry and the gauging. We then study in full detail the simplest case of quaternionic manifolds of dimension four with at least one isometry, for which there exists a general parametrization, and study two types of truncations defining Kahler submanifolds of dimension two. As an application, we finally discuss the case of the universal hypermultiplet of N=2 superstrings and its truncations to the dilaton chiral multiplet of N=1 superstrings. We argue that de Sitter vacua in such theories are necessarily unstable in weakly coupled situations, while they can in principle be metastable in strongly coupled regimes.

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