论文标题
在类型IIA广告上$ _3 $解决方案和巨大的GK几何形状
On Type IIA AdS$_3$ solutions and massive GK geometries
论文作者
论文摘要
我们为扭曲广告提供必要的条件$ _3 $（和Mink $ _3 $）的II型超级解决方案，以保留$ {\ cal N} =（2,0）$ supersymmetry，就其内部空间M $ _7 $而言。这样的解决方案具有规范的十维杀戮载体，可能是时间样或无效的。在这项工作中，我们将无效的IIA型超重力分类为NULL外壳，这使得M $ _7 $ $ _7 $将其作为圆纤维在六维基础上，带有正交SU（2）结构，其中包含一个复杂的四个manifold。我们将重点缩小到$ $ _7 $变为$ \ mathbb {t}^2 $ fibred在kähler歧管上的解决方案。我们找到一类解决方案，这些解决方案是GK几何形式的大型IIA版本，并提出了一个极端问题，该问题仅使用拓扑来计算解决方案的中心电荷。最后，我们提出了ADS $ _3 $解决方案的几何条件，以保存任意扩展手性超对称性。
We give the necessary and sufficient conditions for warped AdS$_3$ (and Mink$_3$) solutions of Type II supergravities to preserve ${\cal N}=(2,0)$ supersymmetry, in terms of geometric conditions on their internal space M$_7$. Such solutions possess a canonical ten-dimensional Killing vector that can be either time-like or null. In this work we classify the null case in massive Type IIA supergravity which necessitates that M$_7$ decomposes as a circle fibration over a six-dimensional base with orthogonal SU(2)-structure containing a complex four-manifold. We narrow our focus to solutions for which M$_7$ becomes $\mathbb{T}^2$ fibred over a foliation of a Kähler manifold over an interval. We find a class of solutions which are the massive Type IIA version of GK geometries and present an extremal problem which computes the central charge of the solution using just topology. Finally, we present geometric conditions for AdS$_3$ solutions to preserve arbitrary extended chiral supersymmetry.
