We use the variational principle approach to derive the large $N$ holographic dictionary for two-dimensional $T\bar T$-deformed CFTs, for both signs of the deformation parameter. The resulting dual gravitational theory has mixed boundary conditions for the non-dynamical graviton; the boundary conditions for matter fields are undeformed. When the matter fields are turned off and the deformation parameter is negative, the mixed boundary conditions for the metric at infinity can be reinterpreted on-shell as Dirichlet boundary conditions at finite bulk radius, in agreement with a previous proposal by McGough, Mezei and Verlinde. The holographic stress tensor of the deformed CFT is fixed by the variational principle, and in pure gravity it coincides with the Brown-York stress tensor on the radial bulk slice with a particular cosmological constant counterterm contribution. In presence of matter fields, the connection between the mixed boundary conditions and the radial "bulk cutoff" is lost. Only the former correctly reproduce the energy of the bulk configuration, as expected from the fact that a universal formula for the deformed energy can only depend on the universal asymptotics of the bulk solution, rather than the details of its interior. The asymptotic symmetry group associated with the mixed boundary conditions consists of two commuting copies of a state-dependent Virasoro algebra, with the same central extension as in the original CFT.

中文翻译：

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$ T \ bar T $和批量切除的海市rage楼

对于变形参数的两个符号，我们使用变分原理方法为二维$ T \ bar T $变形的CFT导出大型$ N $全息词典。由此产生的双重引力理论具有非动力引力的混合边界条件。物质场的边界条件不变。当物质场关闭且变形参数为负时，可以将无穷大度量的混合边界条件在壳上重新解释为有限体积半径下的Dirichlet边界条件，这与McGough，Mezei和Verlinde先前的建议一致。变形CFT的全息应力张量通过变分原理固定，在纯重力作用下，它与径向体积切片上的Brown-York应力张量重合，具有特定的宇宙学常数反项贡献。在存在物质场的情况下，混合边界条件和径向“体截止”之间的连接丢失。从变形能量的通用公式只能取决于本体溶液的通用渐近性，而不是其内部的细节这一事实可以预料，只有前者才能正确地复制本体结构的能量。与混合边界条件相关的渐近对称群由状态依赖的Virasoro代数的两个可交换副本组成，其中心扩展与原始CFT中的扩展相同。混合边界条件和径向“体截止”之间的联系丢失了。从变形能量的通用公式只能取决于本体溶液的通用渐近性，而不是其内部的细节这一事实可以预料，只有前者才能正确地复制本体结构的能量。与混合边界条件相关的渐近对称群由状态依赖的Virasoro代数的两个可交换副本组成，其中心扩展与原始CFT中的扩展相同。混合边界条件和径向“体截止”之间的联系丢失了。从变形能量的通用公式只能取决于本体溶液的通用渐近性，而不是其内部的细节这一事实可以预料，只有前者才能正确地复制本体结构的能量。与混合边界条件相关的渐近对称群由状态依赖的Virasoro代数的两个可交换副本组成，其中心扩展与原始CFT中的扩展相同。