Conformally soft photons and gravitons

DOI10.1007/JHEP01(2019)184zbMATH Open1409.81116arXiv1810.05219OpenAlexW3101597000WikidataQ128535937 ScholiaQ128535937MaRDI QIDQ667271

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Publication date: 12 March 2019

Published in: (Search for Journal in Brave)

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 $SL(2,mathbbC)$ Lorentz quantum numbers: namely their conformal scaling dimension and spin $$ instead of the energy and momentum. This characterization precludes the notion of a soft particle whose energy is taken to zero. We propose it should be replaced by the notion of a conformally soft particle with $h=0$ or $$. For photons we explicitly construct conformally soft $SL(2,mathbbC)$ 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 $(2,0)$ $SL(2,mathbbC)$ primary wavefunction. Interestingly, BMS supertranslations are generated by a spin-one weight $(frac32,frac12)$ operator, which nevertheless shares holomorphic characteristics of a conformally soft operator. This is because the right hand side of its OPE with a weight $$ operator $$ involves the shifted operator $$. 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.

Full work available at URL: https://arxiv.org/abs/1810.05219

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