Long-Range Interactions in Celestial CFT

TL;DR

This paper investigates how loop corrections in QED and gravity influence celestial conformal field theories, revealing that logarithmic soft theorems exponentiate and are rooted in long-range gauge interactions, affecting the structure of soft operator algebras.

Contribution

It demonstrates the exponentiation of logarithmic soft factors in celestial CFT and introduces conformally soft loop operators with their OPEs and Ward identities.

Findings

Logarithmic soft factors exponentiate, indicating non-independent multi-particle effects.

Long-range gauge interactions govern the structure of soft theorems at loop level.

Non-local Ward identities reflect pair-wise gauge boson exchanges between operators.

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.