$T\bar{T}$、缠结楔截面和分裂性质的破坏
$T\bar{T}$, the entanglement wedge cross section, and the breakdown of the split property
摘要：
我们考虑细粒度探针的纠缠结构的二维共形场论变形的不相关的双迹运营商$T\bar{T}$和它的密切相关的，但不同的单迹对应。对于全息共形场论，这些变形可以解释为在反德西特空间的紫外区域中的体物理的修改。因此，我们可以使用Ryu-Takayanagi公式及其对混合态纠缠度量的推广来检验高度非平凡的一致性条件。一般来说，体量和边界量之间的一致性要求任意亏格流形上的配分函数是等价的。对于单迹变形，这是一个渐进线性的双曲子几何，我们发现，互信息和反射熵发散不相交的间隔时，分离距离接近一个最小的，有限的值，仅取决于变形参数。这意味着互信息不能作为一个几何调节器，这是有关的分裂性质的故障在逆Hagedorn温度。相反，对于双迹变形，这是对偶的反德西特空间与有限的径向截止，我们发现所有的分歧消失，包括标准的量子场论紫外线发散，一般被视为不相交的间隔变得相邻。在此基础上，我们利用共形微扰理论计算了反射熵。虽然我们发现体积和边界计算之间的形式上类似的行为，我们发现定量不同的结果。我们对这些分歧的解释和必须改变以恢复一致性的物理学进行评论。我们还简要地讨论了$T{\bar J}$和$J{\bar T}$变形。
英文摘要：
We consider fine-grained probes of the entanglement structure of two dimensional conformal field theories deformed by the irrelevant double-trace operator $T\bar{T}$ and its closely related but nonetheless distinct single-trace counterpart. For holographic conformal field theories, these deformations can be interpreted as modifications of bulk physics in the ultraviolet region of anti-de Sitter space. Consequently, we can use the Ryu-Takayanagi formula and its generalizations to mixed state entanglement measures to test highly nontrivial consistency conditions. In general, the agreement between bulk and boundary quantities requires the equivalence of partition functions on manifolds of arbitrary genus. For the single-trace deformation, which is dual to an asymptotically linear dilaton geometry, we find that the mutual information and reflected entropy diverge for disjoint intervals when the separation distance approaches a minimum, finite value that depends solely on the deformation parameter. This implies that the mutual information fails to serve as a geometric regulator which is related to the breakdown of the split property at the inverse Hagedorn temperature. In contrast, for the double-trace deformation, which is dual to anti-de Sitter space with a finite radial cutoff, we find all divergences to disappear including the standard quantum field theory ultraviolet divergence that is generically seen as disjoint intervals become adjacent. We furthermore compute reflected entropy in conformal perturbation theory. While we find formally similar behavior between bulk and boundary computations, we find quantitatively distinct results. We comment on the interpretation of these disagreements and the physics that must be altered to restore consistency. We also briefly discuss the $T{\bar J}$ and $J{\bar T}$ deformations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
