The structure of IR divergences in celestial gluon amplitudes

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.

28 pages, no figures (v2: minor corrections, references added)

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• Loop-level gluon OPEs in celestial holography
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• Celestial Superamplitudes
• Quantizing Carrollian field theories
• (Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes
• The Holographic Soft $S$-Matrix in QED and Gravity
• Celestial IR divergences in general most-subleading-color gluon and gravity amplitudes
• Zwanziger's pairwise little group on the celestial sphere
• An On-Shell Derivation of the Soft Effective Action in Abelian Gauge Theories
• Charge algebra for non-abelian large gauge symmetries at $O(r)$
• Non-abelian soft radiation data for a celestial theory