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Topological and time dependence of the action-complexity relation

机译:动作复杂性关系的拓扑和时间依赖性

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We consider the dependence of the recently proposed action/complexity duality conjecture on time and on the underlying topology of the bulk spacetime. For the former, we compute the dependence of the CFT complexity on a boundary temporal parameter and find it to be commensurate with corresponding computations carried out in terms of the rate of change of the bulk action on a Wheeler deWitt (WDW) patch. For the latter, we compare the action/complexity relation for ( d + 1 )-dimensional Schwarzschild AdS black holes to those of their geon counterparts, obtained via topological identification in the bulk spacetime. The complexity/action duality relation holds in both cases, but with the proportionality changed by a factor of 4, indicating sensitivity to spacetime topology.
机译:我们考虑了最近提出的动作/复杂性对偶性猜想对时间和整体时空的基础拓扑的依赖。对于前者,我们计算了CFT复杂度对边界时间参数的依赖性,并发现它与在Wheeler deWitt(WDW)贴片上的整体作用变化率方面进行的相应计算相称。对于后者,我们将(d +1)维Schwarzschild AdS黑洞与其geon对应物的作用/复杂度关系进行了比较,这是通过整体时空中的拓扑识别获得的。在这两种情况下,复杂度/动作对偶关系都成立,但是比例改变了4倍,表明对时空拓扑敏感。

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