论文标题
截止广告的共形边界条件$ _3 $
Conformal Boundary Conditions from Cutoff AdS$_3$
论文作者
论文摘要
我们在圆环上的2D欧几里得QFT的空间中构造了一个特定的流动，我们认为这对3D Euclidean重力中的一类溶液是双重的，并具有共形边界条件。这种新的流程来自内核的传统变换，该转换实现了$ t \ bar {t} $变形，并且是由于需要在欧几里得重力中的边界条件以椭圆形的边界条件而动机，即它们具有明确定义的繁殖物来进行度量波动。我们证明了在所谓的常数平均曲率（CMC）切片中，我们的流程方程与Wheeler De-Witt方程的变体之间的等效性。我们得出流量的内核，并在低温极限下计算相应的基态能量。一旦固定变形参数，只要种子理论是CFT，基态的存在就独立于初始数据。状态的高温密度具有类似心脏的行为，而不是$ t \ bar {t} $变形理论的Hagedorn生长特征。
We construct a particular flow in the space of 2D Euclidean QFTs on a torus, which we argue is dual to a class of solutions in 3D Euclidean gravity with conformal boundary conditions. This new flow comes from a Legendre transform of the kernel which implements the $T\bar{T}$ deformation, and is motivated by the need for boundary conditions in Euclidean gravity to be elliptic, i.e. that they have well-defined propagators for metric fluctuations. We demonstrate equivalence between our flow equation and variants of the Wheeler de-Witt equation for a torus universe in the so-called Constant Mean Curvature (CMC) slicing. We derive a kernel for the flow, and we compute the corresponding ground state energy in the low-temperature limit. Once deformation parameters are fixed, the existence of the ground state is independent of the initial data, provided the seed theory is a CFT. The high-temperature density of states has Cardy-like behavior, rather than the Hagedorn growth characteristic of $T\bar{T}$-deformed theories.
