论文标题
在弯曲的三个manifolds上的非相关性超对称性
Non-Relativistic Supersymmetry on Curved Three-Manifolds
论文作者
论文摘要
我们在弯曲的牛顿 - 卡丹三序中构建了非相对性超对称场理论的明确示例。这些结果是通过在Lorentzian歧管上的四维超对称场理论和其超对称参数遵守的杀伤旋转方程式获得的无效降低。这引起了一组代数和差异杀伤旋转方程，这些方程式被所得的三维非相关场理论的超对称参数所遵循。我们得出了必要和充分的条件，这些条件确定了牛顿 - 卡丹背景是否接受这些杀戮旋转方程的非平凡解。讨论了遵守这些条件的牛顿 - 卡丹背景的两个示例。一流的特征是可整合的叶片，对应于所谓的无扭转扭转几何形状，并包括歧管，其空间切片与庞加莱盘是同构。第二类示例具有不可融合的叶面结构，对应于接触歧管。
We construct explicit examples of non-relativistic supersymmetric field theories on curved Newton-Cartan three-manifolds. These results are obtained by performing a null reduction of four-dimensional supersymmetric field theories on Lorentzian manifolds and the Killing spinor equations that their supersymmetry parameters obey. This gives rise to a set of algebraic and differential Killing spinor equations that are obeyed by the supersymmetry parameters of the resulting three-dimensional non-relativistic field theories. We derive necessary and sufficient conditions that determine whether a Newton-Cartan background admits non-trivial solutions of these Killing spinor equations. Two classes of examples of Newton-Cartan backgrounds that obey these conditions are discussed. The first class is characterised by an integrable foliation, corresponding to so-called twistless torsional geometries, and includes manifolds whose spatial slices are isomorphic to the Poincaré disc. The second class of examples has a non-integrable foliation structure and corresponds to contact manifolds.
