Reparametrization modes in 2d CFT and the effective theory of stress tensor exchanges

Abstract

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.

arXiv comment18 pages, 2 figures. v3: matches published version

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• Non-local reparametrization action in coupled Sachdev-Ye-Kitaev models
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• Virasoro blocks and the reparametrization formalism
• Toward Null State Equations in $d>2$
• Resummation of Multi-Stress Tensors in Higher Dimensions
• Operator growth and black hole formation
• Conformal Blocks and Bilocal Vertex Operator Transition Amplitudes
• Universal thermalization dynamics in (1+1)d QFTs