Non-abelian soft radiation data for a celestial theory

TL;DR

This work translates extensive perturbative data on soft radiation in non-abelian gauge theories into the celestial CFT framework to test and constrain the proposed celestial theory. It shows that all logarithms in the single-emission current can be reabsorbed into the running of the $d$-dimensional coupling evaluated at dipole scales, challenging the necessity of a strictly logarithmic celestial theory. The analysis of double and triple soft currents reveals that celestial OPEs are unambiguous in some helicity sectors but depend on gluon energy fractions in others, with associativity holding in same-helicity cases but failing in mixed-helicity configurations unless one imposes strongly ordered limits, which themselves introduce ambiguities. Collectively, these results provide data-driven constraints on the structure of the celestial theory and indicate that either a generalized CCFT (beyond the free-boson model) or additional boundary operators may be required to accommodate the full infrared structure of non-abelian gauge theories.

Abstract

Celestial holography posits that the long-distance behavior of gauge and gravity theories is dictated by two-dimensional conformal field theories defined on the celestial sphere. For non-abelian gauge theories, this proposal is verified, to all perturbative orders, by dipole color correlations in the infrared factor of non-abelian scattering amplitudes, which are given by a correlator of matrix-valued vertex operators in a free-boson theory on the sphere. Decades of high-order gauge-theory calculations have provided a number of further results that can be used to test and constrain a possible celestial theory: they include explicit expressions for soft emission currents up to three particles, and up to three loops for single soft emission. In this paper, we analyze this trove of data, appropriately translated in the celestial language, and we use them to extract information on the celestial theory. In particular, we show that all logarithms arising in the loop expansion of the single soft current can be reabsorbed in the scale choices for the $d$-dimensional coupling, casting some doubt on the need for a logarithmic celestial theory. We then note that the celestial OPEs suggested by the structure of multiple emission currents in collinear limits are never ambiguous, but involve coefficients depending on gluon energy fractions, which break holomorphic factorization, as well as associativity when double limits are taken. Strongly-ordered soft limits recover associativity, but suffer from ambiguities already discussed in earlier literature.