Towards Gravity From a Color Symmetry

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 $N\to \mathrm{\infty }$ limit the gauge group corresponds to $w_{1+\mathrm{\infty }}$, 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 $w_{1+\mathrm{\infty }}$. Focusing on MHV amplitudes, main examples are a BCFW type recursion relation and holomorphic three-point amplitudes.