General relativity as a two-dimensional CFT

TL;DR

This paper proposes a novel formulation of general relativity as a two-dimensional conformal field theory, revealing a new perspective on Einstein's equations through on-shell amplitude simplicity.

Contribution

It introduces a two-dimensional CFT framework for GR, connecting scattering amplitudes to a solvable conformal field theory and deriving Einstein's equations as quantum consistency conditions.

Findings

Tree-level amplitudes exhibit remarkable simplicity.

GR can be reformulated as a solvable 2D CFT.

Einstein equations emerge from quantum consistency.

Abstract

The tree-level scattering amplitudes of general relativity encode the full non-linearity of the Einstein field equations. Yet remarkably compact expressions for these amplitudes have been found which seem unrelated to a perturbative expansion of the Einstein-Hilbert action. This suggests an entirely different description of GR which makes this on-shell simplicity manifest. Taking our cue from the tree-level amplitudes, we discuss how such a description can be found. The result is a formulation of GR in terms of a solvable two-dimensional CFT, with the Einstein equations emerging as quantum consistency conditions.