Conformally soft photons and gravitons

By L. Donnay, Andrea Puhm, Andrew Strominger. Journal of High Energy Physics, 2018

190 citations recorded by the source corpus.

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, ℂ) Lorentz quantum numbers: namely their conformal scaling dimension and spin h±h¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ h\pm \overline{h} $$\end{document} 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 h¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{h} $$\end{document} = 0. For photons we explicitly construct conformally soft SL(2, 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, ℂ) primary wavefunction. Interestingly, BMS supertranslations are generated by a spin-one weight (32\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \frac{3}{2} $$\end{document}, 12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \frac{1}{2} $$\end{document}) 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, h¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{h} $$\end{document}) operator Oh,h¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathcal{O}}_{h,\overline{h}} $$\end{document} involves the shifted operator Oh+12,h¯+12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathcal{O}}_{h+\frac{1}{2},\overline{h}+\frac{1}{2}} $$\end{document}. This OPE relation looks quite unusual from the celestial CFT2 perspective but is equivalent to the leading soft graviton theorem and may usefully constrain celestial correlators in quantum gravity.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/718e6f85a393f0146303ed1890f29034ed16a322

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Citations in the corpus

Celestial amplitudes and conformal soft theorems (2019, background): “between conformally soft wavefunctions and asymptotic symmetries [22, 24], although the origins of this connection seem more obscure.”
Bridging Carrollian and celestial holography (2022, background): “The soft photon theorem can be rewritten as a U(1) Kac-Moody Ward identity [69,110,126]”
Holographic symmetry algebras for gauge theory and gravity (2021, background): “This tower is likely not yet the complete celestial symmetry algebra, which may also include Goldstone currents [14,22,32,60] and negative helicity gluon and graviton generators or their shadows.”
Celestial operator products of gluons and gravitons (2019, unknown): “In a conformal basis, this symmetry shifts the operator dimension [8,22]: δPO ±a ∆ (z, z̄) = O ±a ∆+1(z, z̄).”
Conformally soft theorem in gauge theory (2019, background): “Recently there has been interest in and explicit construction of amplitudes in a conformal basis on the celestial sphere [1–16], in which the conformal action is trivial but translation invariance is hidden.”