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Towards Gravity From a Color Symmetry

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arxiv 2209.00696 v1 pith:3XTP3OC5 submitted 2022-09-01 hep-th nlin.SI

classification hep-thnlin.SI
keywords amplitudescelestialinftyexpansiongroupholographickac-moodysphere
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 4 Pith papers

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  3. Generating Hodges' Graviton MHV Formula with an $Lw_{1+\infty}$ Ward Identity

    hep-th 2025-06 accept novelty 6.0 of 10

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  4. Celestial Chiral Algebras and Self-Dual Gravity

    hep-th 2025-07 conditional novelty 4.0 of 10

    This thesis derives deformations of celestial chiral algebras in self-dual gravity on curved backgrounds, obtaining W(infinity) on Eguchi-Hanson space, Ldiff_q(C) under Moyal deformation, and a two-parameter deformati...

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