We analyze a simple example of a holographically dual pair in which we topologically twist both theories. The holography is based on the two-dimensional N = 2 supersymmetric Liouville conformal field theory that defines a unitary bulk quantum supergravity theory in three-dimensional anti-de Sitter space. The supersymmetric version of three-dimensional Liouville quantum gravity allows for a topological twist on the boundary and in the bulk. We define the topological bulk supergravity theory in terms of twisted boundary conditions. We corroborate the duality by calculating the chiral configurations in the bulk supergravity theory and by quantizing the solution space. Moreover, we note that the boundary calculation of the structure constants of the chiral ring carries over to the bulk theory as well. We thus construct a topological AdS/CFT duality in which the bulk theory is independent of the boundary metric.

中文翻译：

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纯粹而扭曲的全息

我们分析了一个简单的全息对偶示例，其中我们在拓扑上扭曲了这两种理论。全息术基于二维 N = 2 超对称刘维尔共形场理论，该理论定义了三维反德西特空间中的整体量子超引力理论。三维 Liouville 量子引力的超对称版本允许在边界和体积上发生拓扑扭曲。我们根据扭曲边界条件定义拓扑体超重力理论。我们通过计算体超重力理论中的手征构型和量化解空间来证实对偶性。此外，我们注意到手性环结构常数的边界计算也适用于体理论。