论文标题
汉密尔顿 - 雅各比方程和全息重新归一化组在球体上流动
The Hamilton-Jacobi Equation and Holographic Renormalization Group Flows on Sphere
论文作者
论文摘要
我们研究了将现场理论放在球体上并打开质量术语时，研究与全息重新归一化组相关的有效机械作用的汉密尔顿 - 雅各比的公式。尽管该系统是超对称的，并且由超电势描述，但是当AD弯曲的边界弯曲时，汉密尔顿的特征功能不容易由超电势给出。我们提出了一种将解决方案构造为标量场自由度的串联扩展的方法。系数是通过将ANSATZ取代为汉密尔顿 - 雅各比方程时获得的差分方程来确定的扭曲因子的函数。我们还展示了如何从BPS方程得出的解决方案而无需求解微分方程。特征函数很容易提供有关全息反应的信息，这些信息取消了广告边界附近的壳动作的差异。
We study the Hamilton-Jacobi formulation of effective mechanical actions associated with holographic renormalization group flows when the field theory is put on the sphere and mass terms are turned on. Although the system is supersymmetric and it is described by a superpotential, Hamilton's characteristic function is not readily given by the superpotential when the boundary of AdS is curved. We propose a method to construct the solution as a series expansion in scalar field degrees of freedom. The coefficients are functions of the warp factor to be determined by a differential equation one obtains when the ansatz is substituted into the Hamilton-Jacobi equation. We also show how the solution can be derived from the BPS equations without having to solve differential equations. The characteristic function readily provides information on holographic counterterms which cancel divergences of the on-shell action near the boundary of AdS.
