Towards Gravity From a Color Symmetry

TL;DR

This paper proposes a holographic approach to gravity using color-kinematics duality and celestial CFT, revealing connections between gauge symmetries, emergent momentum space, and gravitational amplitudes.

Contribution

It introduces a novel construction of gravitational amplitudes via a 2D Kac-Moody theory on the celestial sphere, linking gauge symmetries to gravity in a holographic framework.

Findings

Emergence of 4D momentum space from celestial CFT

Connection between Kac-Moody currents and gravitational amplitudes

Recursion relations for MHV amplitudes

Abstract

Using tools from color-kinematics duality we propose a holographic construction of gravitational amplitudes, based on a 2d Kac-Moody theory on the celestial sphere. In the $N\to \infty$ limit the gauge group corresponds to $w_{1+\infty}$, due to the $U(N)$ generators enjoying a simple quantum group structure, which is in turn inherited from a twistor fiber over the celestial sphere. We show how four-dimensional momentum-space is emergent in this picture, which connects directly to the so-called kinematic algebra of the tree-level S-Matrix. On the other hand, the framework can be embedded within a celestial CFT to make contact with holographic symmetry algebras previously observed in the soft expansion. Kac-Moody currents play the role of a graviton to all orders in such expansion, and also lead to a natural notion of Goldstone modes for $w_{1+\infty}$. Focusing on MHV amplitudes, main examples are a BCFW type recursion relation and holomorphic three-point amplitudes.