Virasoro blocks and the reparametrization formalism
arXiv:2212.02527 · doi:10.1007/JHEP04(2023)143
Abstract
An effective theory designed to compute Virasoro identity blocks at large central charge, expressed in terms of the propagation of a reparametrization/shadow mode between bilocal vertices, was recently put forward. In this paper I provide the formal theoretical framework underlying this effective theory by reformulating it in terms of standard concepts : conformal geometry, generating functionals and Feynman diagrams. A key ingredient to this formalism is the bilocal vertex operator, or reparametrized two-point function, which is shown to generate arbitrary stress tensor insertions into a two-point function of reference. I also suggest an extension of the formalism designed to compute generic Virasoro blocks.
arXiv comment16 pages. v2: comments added, corrected typos
References in corpus (17)
- Gauge Theory Correlators from Non-Critical String Theory
- A bound on chaos
- Black holes and the butterfly effect
- The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
- Conformal Four Point Functions and the Operator Product Expansion
- Conformal Partial Waves and the Operator Product Expansion
- Two-dimensional conformal field theory and the butterfly effect
- A theory of reparameterizations for AdS gravity
- Effective Field Theory for Chaotic CFTs
- Conformal Blocks for Arbitrary Spins in Two Dimensions
- Exact Virasoro Blocks from Wilson Lines and Background-Independent Operators
- Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs
- On the Virasoro six-point identity block and chaos
- Generating Functional in CFT and Effective Action for Two-Dimensional Quantum Gravity on Higher Genus Riemann Surfaces
- Holographic boundary actions in AdS/CFT revisited
- Reparametrization modes in 2d CFT and the effective theory of stress tensor exchanges
- Conformal Blocks and Bilocal Vertex Operator Transition Amplitudes