论文标题
相互作用重力的现场理论
Field Theory of Interacting Boundary Gravitons
论文作者
论文摘要
纯三维重力是一种可重新夸大的理论，其两个免费参数标记为$ g $和$λ$。结果，ADS $ _3 $中边界应力张量的相关函数是根据一个无量纲参数唯一固定的，这是Virasoro代数的中心电荷。同样的论点意味着在有限的径向截止下的ADS $ _3 $重力是一种可误算理论，但现在有一个附加参数对应于截止位置。假设这种理论实际上存在，则该理论对$ t \ overline {t} $ - 变形的CFT是双重偶然的。为了阐明这一点，我们研究了生活在截止平面边界上的边界引力的量子理论以及边界应力张量的相关功能。我们将应力张量相关函数计算为两回路顺序（$ g $是循环计数参数），从而扩展了现有的树级别的结果。这是可行的，这是因为边界引力行动在制作出明智的领域重新定义并变成Nambu-Goto动作的情况下大大简化了这一事实。强加了洛伦兹的不变性后，发现该顺序的相关器是明确的，直到单个不确定的重量化参数。
Pure three-dimensional gravity is a renormalizable theory with two free parameters labelled by $G$ and $Λ$. As a consequence, correlation functions of the boundary stress tensor in AdS$_3$ are uniquely fixed in terms of one dimensionless parameter, which is the central charge of the Virasoro algebra. The same argument implies that AdS$_3$ gravity at a finite radial cutoff is a renormalizable theory, but now with one additional parameter corresponding to the cutoff location. This theory is conjecturally dual to a $T\overline{T}$-deformed CFT, assuming that such theories actually exist. To elucidate this, we study the quantum theory of boundary gravitons living on a cutoff planar boundary and the associated correlation functions of the boundary stress tensor. We compute stress tensor correlation functions to two-loop order ($G$ being the loop counting parameter), extending existing tree level results. This is made feasible by the fact that the boundary graviton action simplifies greatly upon making a judicious field redefinition, turning into the Nambu-Goto action. After imposing Lorentz invariance, the correlators at this order are found to be unambiguous up to a single undetermined renormalization parameter.
