标题： 时空中有界$dS_4$全息术来自$T^2$变形的可解区域 显示英文标题

标题： Timelike-bounded $dS_4$ holography from a solvable sector of the $T^2$ deformation

摘要： 近期的研究利用了$T\bar T$风格变形的可处理性，提出了三维整体时空中的类时边界块，其中包括$dS_3$。 这一过程通过将问题分解为两部分来实现：一个可解理论，捕捉最熵值的能量带，以及一个调节算法以处理额外效应和精细结构。 我们指出，该方法可以轻松扩展到更高维度，并且不需要完全分解$T^2$算符（即[1]中定义的$T\bar T$的高维类比）。 聚焦于$dS_4$，我们首先通过在${S}^2\times \mathbb{R}$上对$CFT_3$的受限$T^2$变形，在有限的$N$条件下定义了一个可解理论，其中$T$被替换为其在对称均匀状态下的形式，该形式仅包含对角能量密度$E/V$和压力（-$dE/dV$）分量。 这定义了$dS_4/\text{deformed-CFT}_3$的一个有限-N 可解扇区，捕获了熵主导能带的径向几何结构和计数，通过态计数再现了 Gibbons-Hawking 熵。 为了准确捕获包括引力子在内的$dS_4$的局域整体激发，我们构建了一个变形算法，直接类比于最近在 [2] 中提出的$dS_3$的情形。 这个过程从一个无穷小的可解变形作为调节量开始。 完整的微观理论通过在每一步添加重新归一化的$T^2$和其他算符来构建，这些算符由与局域整体计算相匹配来定义（当适用时），包括从$AdS_4/CFT_3$到$dS_4$的提升（在 M 理论的双曲紧化中可用）。 局域整体算法的细节取决于边界条件的选择；我们在广义相对论及其扩展中总结了这些情况的状态，通过我们有限量子理论可以 UV 完成的圆柱狄利克雷条件来说明我们的方法。 显示英文摘要

摘要： Recent research has leveraged the tractability of $T\bar T$ style deformations to formulate timelike-bounded patches of three-dimensional bulk spacetimes including $dS_3$. This proceeds by breaking the problem into two parts: a solvable theory that captures the most entropic energy bands, and a tuning algorithm to treat additional effects and fine structure. We point out that the method extends readily to higher dimensions, and does not require factorization of the full $T^2$ operator (the higher dimensional analogue of $T\bar T$ defined in [1]). Focusing on $dS_4$, we first define a solvable theory at finite $N$ via a restricted $T^2$ deformation of the $CFT_3$ on ${S}^2\times \mathbb{R}$, in which $T$ is replaced by the form it would take in symmetric homogeneous states, containing only diagonal energy density $E/V$ and pressure (-$dE/dV$) components. This defines a finite-N solvable sector of $dS_4/\text{deformed-CFT}_3$, capturing the radial geometry and count of the entropically dominant energy band, reproducing the Gibbons-Hawking entropy as a state count. To accurately capture local bulk excitations of $dS_4$ including gravitons, we build a deformation algorithm in direct analogy to the case of $dS_3$ with bulk matter recently proposed in [2]. This starts with an infinitesimal stint of the solvable deformation as a regulator. The full microscopic theory is built by adding renormalized versions of $T^2$ and other operators at each step, defined by matching to bulk local calculations when they apply, including an uplift from $AdS_4/CFT_3$ to $dS_4$ (as is available in hyperbolic compactifications of M theory). The details of the bulk-local algorithm depend on the choice of boundary conditions; we summarize the status of these in GR and beyond, illustrating our method for the case of the cylindrical Dirichlet condition which can be UV completed by our finite quantum theory.