Title: Metastable de Sitter vacua in N=2 to N=1 truncated supergravity Show Chinese title

Title: N=2截断超引力中的亚稳态de Sitter真空

Abstract: 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. Show Chinese abstract

Abstract: 我们研究了在一般从N=2到N=1截断的超引力理论中实现亚稳态de Sitter真空的可能性，并将其与仅含超多重态的N=2理论和仅含手征多重态的N=1理论中的情况进行了比较。在基于四元数流形且具有引力光子规范化的N=2理论中，由于几何学的特殊性质，de Sitter真空必然不稳定。而在基于Kähler流形和超势的N=1理论中，只要几何结构满足某些约束条件且超势可以自由调整，de Sitter真空则可以是亚稳态的。 在从N=2到N=1的截断过程中，关键要求是母理论中的tachyon需要被投影出子理论，从而使原本不稳定的真空状态变为亚稳态真空。我们研究了这一过程发生的条件，并推导了关于几何结构和规范化的亚稳态约束。 我们详细研究了至少有一个等距的四维四元数流形的最简单情形，该情形存在一个通用参数化，并研究了定义二维Kähler子流形的两种截断类型。作为应用，我们最后讨论了N=2超弦的普遍超多重态及其截断到N=1超弦的手征标量多重态的情况。我们认为，在弱耦合情况下，此类理论中的de Sitter真空必然不稳定；然而，在强耦合状态下，它们原则上可以是亚稳态的。