$c$ -映射、Tits Satake子代数和$\mathcal{N}=2$暴胀子势的寻找
The $c$-map, Tits Satake subalgebras and the search for $\mathcal{N}=2$ inflaton potentials
摘要：
在本文中，我们解决的一般问题，包括膨胀模型表现出Starobinsky的潜力（对称）$\mathcal{N}=2$超引力。这是通过测量超多重态扇区的适当阿贝尔等距，然后将所得理论截断为单个标量场来完成的。利用$\mathcal{N}=2$超引力的整体对称群的特征性质，我们能够对截断后可能得到的$α$ -吸引子模型作出一般性的陈述。我们发现，在对称$\mathcal{N}=2$模型组理论约束限制参数$α$的允许值是$α=1,\,\frac{2}{3},\, \frac{1}{3}$。这证实并推广了最近在文献中获得的结果。我们的分析在很大程度上依赖于对称$\mathcal{N}=2$超引力的数学结构，特别是在所谓的$c$映射连接四元数凯勒流形从特殊凯勒流形。一个一般性的声明可能一致截断的规范模型，导致Starobinsky的潜力，需要重要的帮助山雀佐竹普适性类。本文在数学上是独立的，目的是向公众不仅是物理学家，而且是数学家介绍所涉及的数学结构。为此，本文对$\mathcal{N}=2$超重力仪的主要数学结构和一般测量程序作了较详细的评述。
英文摘要：
In this paper we address the general problem of including inflationary models exhibiting Starobinsky-like potentials into (symmetric) $\mathcal{N}=2$ supergravities. This is done by gauging suitable abelian isometries of the hypermultiplet sector and then truncating the resulting theory to a single scalar field. By using the characteristic properties of the global symmetry groups of the $\mathcal{N}=2$ supergravities we are able to make a general statement on the possible $α$-attractor models which can obtained upon truncation. We find that in symmetric $\mathcal{N}=2$ models group theoretical constraints restrict the allowed values of the parameter $α$ to be $α=1,\,\frac{2}{3},\, \frac{1}{3}$. This confirms and generalizes results recently obtained in the literature. Our analysis heavily relies on the mathematical structure of symmetric $\mathcal{N}=2$ supergravities, in particular on the so called $c$-map connection between Quaternionic Kähler manifolds starting from Special Kähler ones. A general statement on the possible consistent truncations of the gauged models, leading to Starobinsky-like potentials, requires the essential help of Tits Satake universality classes. The paper is mathematically self-contained and aims at presenting the involved mathematical structures to a public not only of physicists but also of mathematicians. To this end the main mathematical structures and the general gauging procedure of $\mathcal{N}=2$ supergravities is reviewed in some detail.
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