论文标题
标量调整理论的保形重归其化
Conformal renormalization of scalar-tensor theories
论文作者
论文摘要
我们研究了一个具有共耦合的标量调整理论，其四分之一的潜力具有局部形式的对称性，直到边界项。我们表明，需要恢复完整的局部保形对称性，可以固定呈现壳动作有限的对抗。所得动作的构件是一种共同的协变量张量，它是由公制和标量场构造的，它具有与Weyl Tensor相同的共形重量。这使我们能够以封闭形式获得标量调整扇区的反处理。该动作的共同完整版本的有限性暗示了保形重态性处方的有效性。我们通过添加保形重力作用以及以McDowell-Mansouri形式编写的Einstein-Ads动作来扩展该理论。即使后者打破了保形对称性，我们发现该动作仍被重新归一化，在考虑渐近局部局部抗DE安慰剂溶液时，标量场的适当损失。研究了这些理论中的黑洞溶液，为此，计算了霍金斯温度和分区函数到鞍点近似中的一阶函数，从而提供了这种重新归化方案的具体示例。
We study a conformally coupled scalar-tensor theory with a quartic potential possessing local conformal symmetry up to a boundary term. We show that requiring the restoration of the full local conformal symmetry fixes the counterterms that render the on-shell action finite. The building block of the resulting action is a conformally covariant tensor which is constructed out of the metric and the scalar field and it has the same conformal weight as the Weyl tensor. This allows us to obtain the counterterms for the scalar-tensor sector in a closed form. The finiteness of the conformally complete version of the action is suggestive on the validity of the Conformal Renormalization prescription. We extend this theory by adding the Conformal Gravity action and also the Einstein-AdS action written in McDowell-Mansouri form. Even though the latter breaks the conformal symmetry, we find that the action is still renormalized provided a suitable falloff of the scalar field when considering asymptotically locally anti-de Sitter solutions. Black hole solutions in these theories are studied, for which the Hawking temperature and the partition function to first order in the saddle-point approximation are calculated, providing a concrete example of this renormalization scheme.
