论文标题
$ t \ bar {t} $变形的随机边界几何和重力二
Random Boundary Geometry and Gravity Dual of $T\bar{T}$ Deformation
论文作者
论文摘要
我们研究了Cardy开发的2D共形场理论的$ t \ bar {t} $变形的随机几何方法，并在重力双重双重偶发中讨论了其实现。在此表示中，$ t \ bar {t} $变形的重力双重双重变形成为现场理论语言的直接翻译。也就是说，双几何形状是ADS $ _3 $空间或BTZ黑洞的合奏，没有有限的截止，但具有随机波动的边界差异性。这反映了重新归一化组的自由度增加，而无关的$ t \ bar {t} $ operator。我们简化了计算方法，并以可以直接转化为重力双语言的方式来计算能量谱和热自由能。我们进一步将这种方法推广到相关函数，并通过Cardy以不同的方法计算的通用对数校正来重现全阶结果。与较早的提案相反，此版本的$ t \ bar {t} $变形的重力双重偶性不仅适用于能量谱和热自由能，而且对相关函数也有效。
We study the random geometry approach to the $T\bar{T}$ deformation of 2d conformal field theory developed by Cardy and discuss its realization in a gravity dual. In this representation, the gravity dual of the $T\bar{T}$ deformation becomes a straightforward translation of the field theory language. Namely, the dual geometry is an ensemble of AdS$_3$ spaces or BTZ black holes, without a finite cutoff, but instead with randomly fluctuating boundary diffeomorphisms. This reflects an increase in degrees of freedom in the renormalization group flow to the UV by the irrelevant $T\bar{T}$ operator. We streamline the method of computation and calculate the energy spectrum and the thermal free energy in a manner that can be directly translated into the gravity dual language. We further generalize this approach to correlation functions and reproduce the all-order result with universal logarithmic corrections computed by Cardy in a different method. In contrast to earlier proposals, this version of the gravity dual of the $T\bar{T}$ deformation works not only for the energy spectrum and the thermal free energy but also for correlation functions.
