We study the origin of the recently proposed effective theory of stress tensor exchanges based on reparametrization modes, that has been used to efficiently compute Virasoro identity blocks at large central charge. We first provide a derivation of the nonlinear Alekseev-Shatashvili action governing these reparametrization modes, and argue that it should be interpreted as the generating functional of stress tensor correlations on manifolds related to the plane by conformal transformations. In addition, we demonstrate that the rules previously prescribed with the reparametrization formalism for computing Virasoro identity blocks naturally emerge when evaluating Feynman diagrams associated with stress tensor exchanges between pairs of external primary operators. We make a few comments on the connection of these results to gravitational theories and holography.

我们研究了最近基于重参数化模式提出的有效应力张量交换理论的起源，该理论已被用于有效地计算大中心电荷下的Virasoro身份块。我们首先提供控制这些重新参数化模式的非线性Alekseev-Shatashvili动作的推导，并认为应将其解释为通过共形变换在与平面相关的流形上产生应力张量相关性的函数。此外，我们证明，在评估与外部主算子对之间的应力张量交换相关的费曼图时，自然会出现先前由重新参数化形式主义规定的用于计算Virasoro身份块的规则。