论文标题
纯BTZ黑洞微晶格的动作复杂性的正规化
Regularizations of Action-Complexity for a Pure BTZ Black Hole Microstate
论文作者
论文摘要
在动作复杂性提案中，有两种不同的方法可以使重力内壳动作正规化，这在ADS/CFT的框架中等效。在本文中，我们希望研究它们对纯BTZ黑洞微晶格的等效性。微晶格是从由动态的时间型ETW brane截断的双面BTZ黑洞获得的。此外，在二维CFT中，有限的能量纯状态是双重的。我们表明，如果包括一个受全息重新归一化启发的时尚反对，以及在WDW贴片的时尚边界上的Gibbons-Hawking-york术语，其中一种正常化的一种，则在两种方法中的紫外线词的系数中存在，这两种方法是在两种方法中相等的。此外，我们比较了两个正规化的动作复杂性的有限条款，并表明当紫外线截止表面足够接近散装时空的渐近边界时，两种正则化的动作复杂性变得完全均等。
In the action-complexity proposal there are two different methods to regularize the gravitational on-shell action, which are equivalent in the framework of AdS/CFT. In this paper, we want to study the equivalence of them for a pure BTZ black hole microstate. The microstate is obtained from a two-sided BTZ black hole truncated by a dynamical timelike ETW brane. Moreover, it is dual to a finite energy pure state in a two-dimensional CFT. We show that if one includes the timelike counterterms inspired by holographic renormalization as well as the Gibbons-Hawking-York term on the timelike boundary of the WDW patch, which exists in one of the regularizations, the coefficients of the UV divergent terms of action-complexity in the two methods become equal to each other. Furthermore, we compare the finite terms of action-complexity in both regularizations, and show that when the UV cutoff surface is close enough to the asymptotic boundary of the bulk spacetime, action-complexities in both regularizations become exactly equal to each other.
