论文标题
通用长臂猿 - 尤其是具有曲率，扭转和非金属理论的理论术语
Universal Gibbons-Hawking-York term for theories with curvature, torsion and non-metricity
论文作者
论文摘要
通过建立具有非金属和扭转的重力理论的全息重新归一化的动机，我们提出了一种用于计算Gibbons-Hawking-York（GHY）项的新的，有效的一般方法。我们的方法包括通过引入合适的Lagrange倍增器来使曲率，扭转或非金属性的任何非线性组成。此外，我们对差异形式使用拆分形式主义，将它们写成$（n-1）+1 $尺寸。动作的边界条款在这种形式主义中通过Stokes的定理表现出来，以便可以直接读取Dirichlet问题的补偿性术语。我们观察到，仅包含曲率的拉格朗日中的那些术语才会促成Ghy术语。术语仅在扭转和非金属方面的多项式不需要对变异问题的任何ghy术语补偿。我们通过确认Einstein-Hilbert的现有结果和四维Chern-Simons修饰的重力来测试我们的方法。此外，我们为Lovelock-Chern-Simons和度量标准重力获得了新的结果。在所有四个示例中，我们的新方法和结果为ADS/CFT内的自旋和高光电流的系统流体动力扩展提供了新的方法。
Motivated by establishing holographic renormalization for gravitational theories with non-metricity and torsion, we present a new and efficient general method for calculating Gibbons-Hawking-York (GHY) terms. Our method consists of linearizing any nonlinearity in curvature, torsion or non-metricity by introducing suitable Lagrange multipliers. Moreover, we use a split formalism for differential forms, writing them in $(n-1)+1$ dimensions. The boundary terms of the action are manifest in this formalism by means of Stokes' theorem, such that the compensating GHY term for the Dirichlet problem may be read off directly. We observe that only those terms in the Lagrangian that contain curvature contribute to the GHY term. Terms polynomial solely in torsion and non-metricity do not require any GHY term compensation for the variational problem to be well-defined. We test our method by confirming existing results for Einstein-Hilbert and four-dimensional Chern-Simons modified gravity. Moreover, we obtain new results for Lovelock-Chern-Simons and metric-affine gravity. For all four examples, our new method and results contribute to a new approach towards a systematic hydrodynamic expansion for spin and hypermomentum currents within AdS/CFT.
