Non-linear uplift Ansätze for the internal metric and the four-form field-strength of maximal supergravity
Non-linear uplift Ansätze for the internal metric and the four-form field-strength of maximal supergravity
复制标题
内度量和最大超重力四种形式场强的非线性隆起Ansätze
DOI：
10.1007/jhep05(2016)145
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发表时间：
2016
影响因子：
5.4
通讯作者：
O. Krüger
中科院分区：
文献类型：
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作者：
O. Krüger
摘要 文献中对 SO(8) 测量的 N = 8 超重力向 11 维超重力的提升进行了深入研究。它由两种理论各自的矢量场和标量场之间的一致关系给出。例如，最近的工作为内部流形上的标量自由度提供了非线性提升Ansätze：逆度量和具有混合指数结构的三形式通量。然而，人们总是通过反转逆度量来找到紧致流形的度量——这项任务只有在特定情况下才可能实现，例如对于 G2，SO(3)×SO(3) 或 SU(3)×U(1)×U(1) 11 维超重力不变解。在本文中，我根据四维标量和紧致背景流形上的 Killing 形式，提出了一种直接非线性提升 Ansatz 的内部度量。基于这个公式，我还找到了扭曲因子和完整内部三型通量以及内部四型场强的新提升 Ansätze。四维形式的新公式仅取决于度量、通量以及四维标量和背景杀戮形式——不需要计算通量的导数。这项工作中提出的所有 Ansätze 都通过了对 11 维超引力的 G2 不变解的非常重要的测试。我的结果可以推广到其他紧致化，例如从IIB型超重力减少到五维。
A bstractThe uplift of SO(8) gauged N = 8 supergravity to 11-dimensional supergravity is well studied in the literature. It is given by consistent relations between the respective vector and scalar fields of both theories. For example, recent work provided non-linear uplift Ansätze for the scalar degrees of freedom on the internal manifold: the inverse metric and the three-form flux with mixed index structure. However, one always found the metric of the compactified manifold by inverting the inverse metric — a task that was only possible in particular cases, e.g. for the G2, SO(3)×SO(3) or SU(3)×U(1)×U(1) invariant solutions of 11-dimensional supergravity.In this paper, I present a direct non-linear uplift Ansatz for the internal metric in terms of the four-dimensional scalars and the Killing forms on the compactified background manifold. Based on this formula, I also find new uplift Ansätze for the warp factor and the full internal three-form flux, as well as for the internal four-form field-strength. The new formula for the four-form only depends on the metric, the flux as well as the fourdimensional scalars and background Killing forms — it does not require to calculate the derivative of the flux. All the Ansätze presented in this work pass a very non-trivial test for a G2 invariant solution of 11-dimensional supergravity.My results may be generalized to other compactifications, e.g. the reduction from type IIB supergravity to five dimensions.