
Gonzalez, H., A., & Rojas, F. (2021). The structure of IR divergences in celestial gluon amplitudes. J. High Energy Phys., (6), 171.
Abstract: The allloop resummation of SU(N) gauge theory amplitudes is known to factorize into an IRdivergent (soft and collinear) factor and a finite (hard) piece. The divergent factor is universal, whereas the hard function is a processdependent 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 celestialIRsafe 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 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.



Gonzalez, H. A., Puhm, A.,, & Rojas, F. (2020). Loop corrections to celestial amplitudes. Phys. Rev. D., 102, 126027.
Abstract: We study the effect of loop corrections to conformal correlators on the celestial sphere at null infinity. We first analyze finite oneloop celestial amplitudes in pure YangMills theory and Einstein gravity. We then turn to our main focus: infrared divergent loop amplitudes in planar N=4
super–YangMills theory. We compute the celestial oneloop amplitude in dimensional regularization and show that it can be recast as an operator acting on the celestial treelevel amplitude. This extends to any loop order, and the resummation of all planar loops enables us to write down an expression for the allloop celestial amplitude. Finally, we show that the exponentiated allloop expression given by the BernDixonSmirnov (BDS) formula gets promoted on the celestial sphere to an operator acting on the treelevel conformal correlation function, thus yielding, the celestial BDS formula.

