Apruzzi Fabio, Bonetti Federico, García Etxebarria Iñaki, Hosseini Saghar S, Schäfer-Nameki Sakura
Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, Bern, 3012 Switzerland.
Mathematical Institute, University of Oxford, Andrew-Wiles Building, Woodstock Road, Oxford, OX2 6GG UK.
Commun Math Phys. 2023;402(1):895-949. doi: 10.1007/s00220-023-04737-2. Epub 2023 May 26.
We determine the dimensional topological field theory, which encodes the higher-form symmetries and their 't Hooft anomalies for -dimensional QFTs obtained by compactifying M-theory on a non-compact space . The resulting theory, which we call the Symmetry TFT, or SymTFT for short, is derived by reducing the topological sector of 11d supergravity on the boundary of the space . Central to this endeavour is a reformulation of supergravity in terms of differential cohomology, which allows the inclusion of torsion in cohomology of the space , which in turn gives rise to the background fields for discrete (in particular higher-form) symmetries. We apply this framework to 7d super-Yang Mills, where , as well as the Sasaki-Einstein links of Calabi-Yau three-fold cones that give rise to 5d superconformal field theories. This M-theory analysis is complemented with a IIB 5-brane web approach, where we derive the SymTFTs from the asymptotics of the 5-brane webs. Our methods apply to both Lagrangian and non-Lagrangian theories, and allow for many generalisations.
我们确定了维度拓扑场论，它编码了通过在非紧致空间上紧致化M理论得到的d维量子场论的高阶形式对称性及其‘t Hooft反常。由此产生的理论，我们简称为对称拓扑场论（SymTFT），是通过在空间的边界上约化11维超引力的拓扑部分而导出的。这项工作的核心是根据微分上同调对超引力进行重新表述，这允许在空间的上同调中包含挠率，进而产生离散（特别是高阶形式）对称性的背景场。我们将这个框架应用于7维超杨-米尔斯理论，以及产生5维超共形场论的卡拉比-丘三维锥的萨斯卡-爱因斯坦联系。这种M理论分析辅以IIB 5膜网方法，我们从5膜网的渐近性中导出对称拓扑场论。我们的方法适用于拉格朗日理论和非拉格朗日理论，并允许进行许多推广。
