Non-abelian infrared divergences on the celestial sphere

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 $$ \mathcal{N} $$ 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.

“…Therefore, one may ponder on the precise effect this correction has on the celestial side. This has been emphasized in [73] and here we would like to elaborate on it.…”

Section: Final Remarksmentioning

confidence: 82%

The structure of IR divergences in celestial gluon amplitudes

González

Rojas

2021

“…Vertex operators constructed from this boson give the dressing for charged states. In Yang-Mills this gets promoted to a Lie algebra valued free boson [54,55]. The interacting version [5] is described by a Chern-Simons theory on a hyperbolic slice of Minkowski space [4], which should be dual to a Wess-Zumino-Witten model.…”

Section: Jhep11(2021)143mentioning

confidence: 99%

“…See[53][54][55] for recent results on the IR structure of celestial loop amplitudes in non-Abelian gauge theory.…”

mentioning

confidence: 99%

Revisiting the conformally soft sector with celestial diamonds

Pasterski¹,

Puhm

Trevisani

2021

Celestial diamonds encode the structure of global conformal multiplets in 2D celestial CFT and offer a natural language for describing the conformally soft sector. The operators appearing at their left and right corners give rise to conformally soft factorization theorems, the bottom corners correspond to conserved charges, and the top corners to conformal dressings. We show that conformally soft charges can be expressed in terms of light ray integrals that select modes of the appropriate conformal weights. They reside at the bottom corners of memory diamonds, and ascend to generalized currents. We then identify the top corners of the associated Goldstone diamonds with conformal Faddeev-Kulish dressings and compute the sub-leading conformally soft dressings in gauge theory and gravity which are important for finding nontrivial central extensions. Finally, we combine these ingredients to speculate on 2D effective descriptions for the conformally soft sector of celestial CFT.

“…The problem however would be quite challenging, in particular due the appearance of infrared divergences. Here again it may prove useful to establish contact with the celestial CFT methods, which appear well suited for the incorporation of these effects [67][68][69][70].…”

Section: Jhep12(2021)058mentioning

confidence: 99%

Charge algebra for non-abelian large gauge symmetries at O(r)

Campiglia

Peraza

2021

Asymptotic symmetries of gauge theories are known to encode infrared properties of radiative fields. In the context of tree-level Yang-Mills theory, the leading soft behavior of gluons is captured by large gauge symmetries with parameters that are O(1) in the large r expansion towards null infinity. This relation can be extended to subleading order provided one allows for large gauge symmetries with O(r) gauge parameters. The latter, however, violate standard asymptotic field fall-offs and thus their interpretation has remained incomplete. We improve on this situation by presenting a relaxation of the standard asymptotic field behavior that is compatible with O(r) gauge symmetries at linearized level. We show the extended space admits a symplectic structure on which O(1) and O(r) charges are well defined and such that their Poisson brackets reproduce the corresponding symmetry algebra.