Celestial $w_{1+\infty }$ Symmetries from Twistor Space

Abstract

We explain how twistor theory represents the self-dual sector of four dimensional gravity in terms of the loop group of Poisson diffeomorphisms of the plane via Penrose's non-linear graviton construction. The symmetries of the self-dual sector are generated by the corresponding loop algebra $L{w}_{1+\infty }$ of the algebra $w_{1+\infty }$ of these Poisson diffeomorphisms. We show that these coincide with the infinite tower of soft graviton symmetries in tree-level perturbative gravity recently discovered in the context of celestial amplitudes. We use a twistor sigma model for the self-dual sector which describes maps from the Riemann sphere to the asymptotic twistor space defined from characteristic data at null infinity $\mathcal{I}$. We show that the OPE of the sigma model naturally encodes the Poisson structure on twistor space and gives rise to the celestial realization of $L{w}_{1+\infty }$. The vertex operators representing soft gravitons in our model act as currents generating the wedge algebra of $w_{1+\infty }$ and produce the expected celestial OPE with hard gravitons of both helicities. We also discuss how the two copies of $L{w}_{1+\infty }$, one for each of the self-dual and anti-self-dual sectors, are represented in the OPEs of vertex operators of the 4d ambitwistor string.

Dedicated to our friend and mentor Roger Penrose on the occasion of his 90th birthday and the recent award of his Nobel prize in physics

References in corpus (16)

• Lectures on Celestial Amplitudes
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Ambitwistor strings in 4-dimensions
• Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins
• Ambitwistor strings at null infinity and subleading soft limits
• $(2,2)$ Scattering and the Celestial Torus
• Conformal Block Expansion in Celestial CFT
• Perturbative gauge theory at null infinity
• A simple formula for gravitational MHV amplitudes
• Lectures on Celestial Holography
• Celestial operator products from the worldsheet
• Notes on Conformal Soft Theorems and Recursion Relations in Gravity
• Holographic Chiral Algebra: Supersymmetry, Infinite Ward Identities, and EFTs
• Ambidextrous light transforms for celestial amplitudes
• Celestial Holography: Lectures on Asymptotic Symmetries
• Ambitwistor Strings: Worldsheet Approaches to perturbative Quantum Field Theories

Cited by in corpus (11)

• Bridging Carrollian and Celestial Holography
• The partial Bondi gauge: Further enlarging the asymptotic structure of gravity
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• Minimal models of field theories: Chiral Higher Spin Gravity
• Supersymmetric celestial OPEs and soft algebras from the ambitwistor string worldsheet
• Celestial $w_{1+\infty }$ charges and the subleading structure of asymptotically-flat spacetimes
• Asymptotic Higher Spin Symmetries I: Covariant Wedge Algebra in Gravity
• Deformed $w_{1+\infty }$ Algebras in the Celestial CFT
• Radiative Asymptotic Symmetries of 3D Einstein-Maxwell Theory
• Asymptotic Higher Spin Symmetries III: Noether Realization in Yang-Mills Theory
• Celestial Quantum Error Correction I: Qubits from Noncommutative Klein Space