[论文解读] Long-Range Interactions in Celestial CFT

Sangmin Choi, Ameya Kadhe+1 more|arXiv (Cornell University)|Jan 9, 2026

Black Holes and Theoretical Physics被引用 0

一句话总结

该论文分析了长程规范相互作用如何在天体 CFT 中引入普遍的对数软定理塔及其指数化，并推导了 conformally soft 循环算符的非局部 Ward 恒等式和 OPE。

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.

研究动机与目标

• Motivate celestial CFT as a holographic description of quantum gravity in four-dimensional asymptotically flat spacetimes.
• Understand how loop corrections from long-range interactions affect soft theorems and their symmetry interpretation.
• Derive celestial Ward identities and OPEs for conformally soft operators at tree and loop levels.
• Clarify implications for the soft operator algebra and potential connections to asymptotic symmetry algebras like w_{1+∞}.

提出的方法

• Review SL(2, C) symmetry as the organizing principle for celestial CFT and define conformal primary wavefunctions and extrapolate boundary operators.
• Summarize tree- and loop-level soft factorization in scalar QED and gravity, distinguishing universal, symmetry-governed towers.
• Show that the tower of logarithmic soft factors exponentiates and derive its universal, SL(2, C)-covariant form.
• Construct conformally soft loop operators and compute their OPEs on the celestial sphere.
• Derive celestial ward identities from primary descendants and analyze non-locality arising from long-range interactions.
• Discuss implications for the soft operator algebra and loop corrections to OPE structures.

实验结果

研究问题

• RQ1 How do long-range gauge interactions modify the action of asymptotic symmetries on hard operator insertions at loop level?
• RQ2 Do universal towers of logarithmic soft theorems exponentiate in a way analogous to tree-level towers, and how are they encoded in celestial CFT?
• RQ3 What are the conformally soft loop operator OPEs on the celestial sphere, and how do they differ from tree-level OPEs?
• RQ4 What are the implications of loop-induced non-local Ward identities for the celestial symmetry algebra (e.g., w_{1+∞} and its subalgebras)?

主要发现

• The tower of logarithmic soft factors, constrained by SL(2, C) symmetry, exponentiates at universal loop level, indicating a common origin in long-range gauge exchanges.
• At one loop and beyond, the action of symmetry generators on a given hard operator becomes non-local, involving pairwise sums over other hard operators.
• The celestial OPE between conformally soft loop operators vanishes, mirroring the tree-level case in certain respects and raising questions for the full w_{1+∞} structure.
• Conformally soft loop operators can be defined and their OPEs computed, revealing non-local Ward identities that reflect pairwise hard operator interactions.
• There is a distinction between leading soft theorems (tree-exact) and subleading ones, with loop corrections introducing non-trivial structure that informs soft operator algebras.