Conformally Soft Photons and Gravitons

Abstract

The four-dimensional $S$-matrix is reconsidered as a correlator on the celestial sphere at null infinity. Asymptotic particle states can be characterized by the point at which they enter or exit the celestial sphere as well as their $SL(2,\mathbb{C})$ Lorentz quantum numbers: namely their conformal scaling dimension and spin $h\pm \bar{h}$ instead of the energy and momentum. This characterization precludes the notion of a soft particle whose energy is taken to zero. We propose it should be replaced by the notion of a conformally soft particle with $h=0$ or $\bar{h}=0$. For photons we explicitly construct conformally soft $SL(2,\mathbb{C})$ currents with dimensions $(1,0)$ and identify them with the generator of a $U(1)$ Kac-Moody symmetry on the celestial sphere. For gravity the generator of celestial conformal symmetry is constructed from a $(2,0)$ $SL(2,\mathbb{C})$ primary wavefunction. Interestingly, BMS supertranslations are generated by a spin-one weight $(\frac{3}{2},\frac{1}{2})$ operator, which nevertheless shares holomorphic characteristics of a conformally soft operator. This is because the right hand side of its OPE with a weight $(h,\bar{h})$ operator ${\mathcal{O}}_{h,\bar{h}}$ involves the shifted operator ${\mathcal{O}}_{h+\frac{1}{2},\bar{h}+\frac{1}{2}}$. This OPE relation looks quite unusual from the celestial CFT${}_2$ perspective but is equivalent to the leading soft graviton theorem and may usefully constrain celestial correlators in quantum gravity.

arXiv comment23 pages, 1 figure; corrected typos, added references

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• Celestial amplitudes and conformal soft theorems
• Asymptotic Symmetries and Celestial CFT
• The Holographic Nature of Null Infinity
• Celestial Amplitudes from UV to IR
• Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins
• Conformally Soft Theorem In Gravity
• Extended BMS Algebra of Celestial CFT
• Celestial Amplitudes: Conformal Partial Waves and Soft Limits
• BMS Symmetry of Celestial OPE
• MHV Graviton Scattering Amplitudes and Current Algebra on the Celestial Sphere
• Extended Super BMS Algebra of Celestial CFT
• Celestial Diamonds: Conformal Multiplets in Celestial CFT
• Carrollian Approach to $1+3$D Flat Holography
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
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• BMS Flux Algebra in Celestial Holography
• The Soft $\mathcal{S}$-Matrix in Gravity
• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
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• Charge Algebra in Al(A)dS${}_n$ Spacetimes
• Celestial operator products from the worldsheet
• Celestial chiral algebras, colour-kinematics duality and integrability
• Loops on the Celestial Sphere
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• Coadjoint representation of the BMS group on celestial Riemann surfaces
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• Celestial Current Algebra from Low's Subleading Soft Theorem
• Goldilocks Modes and the Three Scattering Bases
• Conformal properties of soft-operators - 1 : Use of null-states
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• Ambidextrous light transforms for celestial amplitudes
• Geometric actions and flat space holography
• Celestial double copy from the worldsheet
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• UV considerations on scattering amplitudes in a web of theories
• On loop celestial amplitudes for gauge theory and gravity
• From Moyal deformations to chiral higher-spin theories and to celestial algebras
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• Celestial Dual Superconformal Symmetry, MHV Amplitudes and Differential Equations
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• From Shockwaves to the Gravitational Memory Effect
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• Symmetries in Celestial CFT${}_d$
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• Missing Corner in the Sky: Massless Three-Point Celestial Amplitudes
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• Kac-Moody symmetry in the light front of gauge theories
• An Infrared On-Shell Action and its Implications for Soft Charge Fluctuations in Asymptotically Flat Spacetimes
• Structure of deformed $w_{1+\infty }$ symmetry and topological generalization in Celestial CFT
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