论文标题
在拉格朗日全息关系上，$ d \ rightarrow2 $和$ 4 $重力极限
On the Lagrangian Holographic Relation at $D\rightarrow2$ and $4$ Limits of Gravity
论文作者
论文摘要
引力拉格朗日可以写成散装和总衍生术语的总结。对于某些重力理论，例如爱因斯坦重力或更一般的lovelock重力，散装和总导数项之间存在拉格朗日全息关系，因此后者由前者完全确定。但是，在$ d \ rightarrow 2 \＆4 $限制下，爱因斯坦或高斯理论的大部分理论本身就是总衍生物。在爱因斯坦和高斯重力上进行Kaluza-klein还原，分别引起了一些二维或四维标量tensor理论。我们获得了$ d = 2 $和$ d = 4 $案例的全息关系，它们的形式与叶子独立形式主义的纯重力中的全息关系相同。
The gravitational Lagrangian can be written as a summation of a bulk and a total derivative term. For some theories of gravity such as Einstein gravity, or more general Lovelock gravities, there are Lagrangian holographic relations between the bulk and the total derivative term such that the latter is fully determined by the former. However at the $D\rightarrow 2\&4$ limit, the bulks of Einstein or Gauss-Bonnet theories become themselves total derivatives. Performing the Kaluza-Klein reduction on Einstein and Gauss-Bonnet gravities gives rise to some two-dimensional or four-dimensional scalar-tensor theories respectively. We obtain the holographic relations for the $D = 2$ and $D = 4$ cases, which have the same form as the holographic relations in pure gravity in the foliation independent formalism.
