The structure of IR divergences in celestial gluon amplitudes

TL;DR

This paper demonstrates that the IR divergence structure of gauge theory amplitudes persists in celestial amplitudes, revealing a universal factorization involving Wilson lines and implications for the convergence of celestial amplitudes.

Contribution

It proves the persistence of IR divergence factorization in celestial amplitudes and characterizes the soft/collinear factor as a scalar correlator of Wilson lines, extending known gauge theory structures.

Findings

IR divergence factorization persists in celestial amplitudes

Soft/collinear factor is a scalar correlator of Wilson lines

Convergence of Mellin transform is ensured by positive cusp anomalous dimension

Abstract

The all-loop resummation of SU$(N)$ gauge theory amplitudes is known to factorize into an IR-divergent (soft and collinear) factor and a finite (hard) piece. The divergent factor is universal, whereas the hard function is a process-dependent quantity. We prove that this factorization persists for the corresponding celestial amplitudes. Moreover, the soft/collinear factor becomes a scalar correlator of the product of renormalized Wilson lines defined in terms of celestial data. Their effect on the hard amplitude is a shift in the scaling dimensions by an infinite amount, proportional to the cusp anomalous dimension. This leads us to conclude that the celestial-IR-safe gluon amplitude corresponds to a expectation value of operators dressed with Wilson line primaries. These results hold for finite $N$. In the large $N$ limit, we show that the soft/collinear correlator can be described in terms of vertex operators in a Coulomb gas of colored scalar primaries with nearest neighbor interactions. In the particular cases of four and five gluons in planar $\mathcal{N}=4$ SYM theory, where the hard factor is known to exponentiate, we establish that the Mellin transform converges in the UV thanks to the fact that the cusp anomalous dimension is a positive quantity. In other words, the very existence of the full celestial amplitude is owed to the positivity of the cusp anomalous dimension.