Long-range interactions in celestial CFT

Abstract

Loop corrections in QED and gravity have recently been conjectured to give rise to an infinite tower of logarithmic soft theorems governing the universal low-energy behavior of photons and gravitons. We explore the implications of this tower for celestial CFT and for the algebra of conformally soft operators. The symmetry-governed part of the tower of logarithmic soft factors is shown to exponentiate, which demonstrates that these loop effects do not represent independent multi-particle interactions, but instead are rooted in the long-range exchange of gauge bosons between pairs of hard operator insertions. We define conformally soft loop operators, and compute their operator product expansions on the celestial sphere. The associated Ward identities exhibit characteristic non-local behaviors, which reflect the pair-wise interactions between hard operator insertions mediated by gauge bosons. We comment on the implications of these results for the soft operator algebra at loop order.

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BibTeX RIS

BibTeX

@article{choi2026longrange,
  title = {{Long-range interactions in celestial CFT}},
  author = {Sangmin Choi and Ameya Kadhe and Andrea Puhm},
  journal = {SciPost Physics},
  year = {2026},
  month = oct,
  doi = {10.21468/scipostphys.21.4.093},
  url = {https://scipost.org/10.21468/SciPostPhys.21.4.093},
  note = {CC BY 4.0},
}

RIS

TY  - JOUR
TI  - Long-range interactions in celestial CFT
AU  - Sangmin Choi
AU  - Ameya Kadhe
AU  - Andrea Puhm
PY  - 2026
DA  - 2026/10/13
JO  - SciPost Physics
DO  - 10.21468/scipostphys.21.4.093
UR  - https://scipost.org/10.21468/SciPostPhys.21.4.093
AB  - Loop corrections in QED and gravity have recently been conjectured to give rise to an infinite tower of logarithmic soft theorems governing the universal low-energy behavior of photons and gravitons. We explore the implications of this tower for celestial CFT and for the algebra of conformally soft operators. The symmetry-governed part of the tower of logarithmic soft factors is shown to exponentiate, which demonstrates that these loop effects do not represent independent multi-particle interactions, but instead are rooted in the long-range exchange of gauge bosons between pairs of hard operator insertions. We define conformally soft loop operators, and compute their operator product expansions on the celestial sphere. The associated Ward identities exhibit characteristic non-local behaviors, which reflect the pair-wise interactions between hard operator insertions mediated by gauge bosons. We comment on the implications of these results for the soft operator algebra at loop order.
SN  - 2542-4653
ER  -

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