The Effective Action of Superrotation Modes

Abstract

Starting from an analysis of four-dimensional asymptotically flat gravity in first order formulation, we show that superrotation reparametrization modes are governed by an Alekseev--Shatashvili action on the celestial sphere. This two-dimensional conformal theory describes spontaneous symmetry breaking of Virasoro superrotations together with the explicit symmetry breaking of more general Diff$({\mathcal{S}}^2)$ superrotations. We arrive at this result by first reformulating the asymptotic field equations and symmetries of the radiative vacuum sector in terms of a Chern--Simons theory at null infinity, and subsequently performing a Hamiltonian reduction of this theory onto the celestial sphere.

arXiv comment40 pages; v2: clarified boundary conditions in section 4, references added; v3: match published version

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Cited by in corpus (27)

• Lectures on Celestial Amplitudes
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• Bridging Carrollian and Celestial Holography
• The partial Bondi gauge: Further enlarging the asymptotic structure of gravity
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
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• BMS Flux Algebra in Celestial Holography
• Revisiting the Conformally Soft Sector with Celestial Diamonds
• Charge Algebra in Al(A)dS${}_n$ Spacetimes
• Carrollian manifolds and null infinity: A view from Cartan geometry
• Coadjoint representation of the BMS group on celestial Riemann surfaces
• Celestial holography on Kerr-Schild backgrounds
• Flat from anti-de Sitter
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• Chaos in Celestial CFT
• Ehlers, Carroll, Charges and Dual Charges
• Reparametrization modes in 2d CFT and the effective theory of stress tensor exchanges
• Higher derivative asymptotic charges and internal Lorentz symmetries
• Celestial IR divergences and the effective action of supertranslation modes
• Mapping SYK to the Sky
• $\widehat{s{l}_2}$ symmetry of ${\mathbb{R}}^{1,3}$ gravity
• The gauging procedure and carrollian gravity