$AdS_3/CFT_2中应力张量的全息环面相关器$ Holographic torus correlators of stress tensor in $AdS_3/CFT_2$

作者:Song He Yi Li Yun-Ze Li Yunda Zhang

在$\rm AdS_3/CFT_2$的背景下,我们研究了环面上共形场论(CFT)应力张量的全息相关器。为了计算应力张量的相关器,我们采用了爱因斯坦-希尔伯特引力理论,并对爱因斯坦方程进行了整体微扰求解。我们提供了一个明确的处方来发展递归关系,使计算更高点的相关器变得简单。相关器和递推关系被发现与CFT中已知的一致。遵循所提出的截止$\rm-AdS$/$T\bar{T}$CFT全息的精神,然后我们扩展我们的计算程序,以研究$\rm-AdS_3$中有限截止处的全息环面相关器。可以获得与较高点相关器相关联的并行递归关系。

In the context of $\rm AdS_3/CFT_2$, we investigate holographic correlators of the stress tensor of a conformal field theory (CFT) on a torus in this work. To calculate the correlators of the stress tensor, we employ the Einstein-Hilbert theory of gravity and perturbatively solve Einstein’s equation in the bulk. We offer an explicit prescription to develop a recurrence relation that makes it simple to compute higher point correlators. The correlators and the recurrence relation are found to be consistent with what is known in CFTs. Following the spirit of the proposed cutoff $\rm AdS$/$T\bar{T}$ CFT holography, we then expand our computation program to investigate holographic torus correlators at a finite cutoff in the $\rm AdS_3$. A parallel recurrence relation associated with higher point correlators can be obtained.



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