Non-abelian soft radiation data for a celestial theory

TL;DR

This paper investigates the structure of non-abelian soft radiation in celestial holography, analyzing high-order gauge theory data to understand the underlying celestial conformal field theory and its properties.

Contribution

It translates high-order gauge theory soft emission data into celestial language, revealing insights into the structure and ambiguities of celestial operator product expansions.

Findings

Logarithms in loop expansions can be absorbed by scale choices, questioning the need for a logarithmic celestial theory.

Celestial OPEs are unambiguous but depend on gluon energy fractions, breaking holomorphic factorization.

Strongly-ordered soft limits restore associativity but introduce ambiguities.

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.