Abstract
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, ℂ) Lorentz quantum numbers: namely their conformal scaling dimension and spin
$$ h\pm \overline{h} $$
h
±
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
$$ \overline{h} $$
h
¯
= 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 (
$$ \frac{3}{2} $$
3
2
,
$$ \frac{1}{2} $$
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,
$$ \overline{h} $$
h
¯
) operator
$$ {\mathcal{O}}_{h,\overline{h}} $$
O
h
,
h
¯
involves the shifted operator
$$ {\mathcal{O}}_{h+\frac{1}{2},\overline{h}+\frac{1}{2}} $$
O
h
+
1
2
,
h
¯
+
1
2
. 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.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
Reference38 articles.
1. D.R. Yennie, S.C. Frautschi and H. Suura, The infrared divergence phenomena and high-energy processes, Annals Phys.
13 (1961) 379 [INSPIRE].
2. S. Weinberg, Infrared photons and gravitons, Phys. Rev.
140 (1965) B516 [INSPIRE].
3. J. de Boer and S.N. Solodukhin, A Holographic reduction of Minkowski space-time, Nucl. Phys.
B 665 (2003) 545 [hep-th/0303006] [INSPIRE].
4. A. Strominger, Asymptotic Symmetries of Yang-Mills Theory, JHEP
07 (2014) 151 [arXiv:1308.0589] [INSPIRE].
5. T. He, P. Mitra and A. Strominger, 2D Kac-Moody Symmetry of 4D Yang-Mills Theory, JHEP
10 (2016) 137 [arXiv:1503.02663] [INSPIRE].
Cited by
117 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献