Curvature squared invariants in six-dimensional ${\cal N} = (1,0)$ supergravity
Curvature squared invariants in six-dimensional ${\cal N} = (1,0)$ supergravity
复制标题
DOI：
--
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
D. Butter;J. Novak;M. Ozkan;Y. Pang;G. Tartaglino-Mazzucchelli
中科院分区：
文献类型：
--
作者：
D. Butter;J. Novak;M. Ozkan;Y. Pang;G. Tartaglino-Mazzucchelli
我们描述了在六维空间中${\cal N}=（1，0）$超引力的几个曲率平方不变量的超对称完备化。不变量的构建是基于超共形张量演算和最近开发的超空间技术之间的密切相互作用，以研究一般的离壳超引力物质耦合。在最小的离壳庞加莱超引力的情况下，基于耦合到线性多重态作为共形补偿器，我们描述了所有三个可能的纯引力曲率平方项在六个维度的离壳超对称完成：黎曼，里奇，和标量曲率平方。这些不变量的线性组合描述了Gauss-Bonnet项的离壳完成，最近在arXiv：1706.09330中提出。我们研究了Einstein-Gauss-Bonnet超引力的性质，它在六维紧致化的$\alpha^\prime$-校正弦理论的有效低能描述中起着核心作用，包括对${\rmAdS}_3\times {\rmS}^3$解的谱的详细分析.我们还提出了一种新的局部超共形不变量的基础上的高导数作用的线性多重态。这个不变量，其中包括引力曲率平方项，可以被定义为耦合到标准外尔多重态或共形超引力的D-Weyl多重态。在第一种情况下，我们展示了如何将这个不变量添加到超对称的爱因斯坦-希尔伯特项中，导致动态生成的宇宙学常数和非超对称（A）dS$_6$解决方案。在Wellon-Weyl多重态中，新的离壳不变量包含Ricci和标量曲率平方项，并且对Wellon-Weyl场具有非平凡依赖性。
We describe the supersymmetric completion of several curvature-squared invariants for ${\cal N}=(1,0)$ supergravity in six dimensions. The construction of the invariants is based on a close interplay between superconformal tensor calculus and recently developed superspace techniques to study general off-shell supergravity-matter couplings. In the case of minimal off-shell Poincar\'e supergravity based on the dilaton-Weyl multiplet coupled to a linear multiplet as a conformal compensator, we describe off-shell supersymmetric completions for all the three possible purely gravitational curvature-squared terms in six dimensions: Riemann, Ricci, and scalar curvature squared. A linear combination of these invariants describes the off-shell completion of the Gauss-Bonnet term, recently presented in arXiv:1706.09330. We study properties of the Einstein-Gauss-Bonnet supergravity, which plays a central role in the effective low-energy description of $\alpha^\prime$-corrected string theory compactified to six dimensions, including a detailed analysis of the spectrum about the ${\rm AdS}_3\times {\rm S}^3$ solution. We also present a novel locally superconformal invariant based on a higher-derivative action for the linear multiplet. This invariant, which includes gravitational curvature-squared terms, can be defined both coupled to the standard-Weyl or dilaton-Weyl multiplet for conformal supergravity. In the first case, we show how the addition of this invariant to the supersymmetric Einstein-Hilbert term leads to a dynamically generated cosmological constant and non-supersymmetric (A)dS$_6$ solutions. In the dilaton-Weyl multiplet, the new off-shell invariant includes Ricci and scalar curvature-squared terms and possesses a nontrivial dependence on the dilaton field.