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...
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doaj-db9b973422f44ec597be21e6eea9c80b2021-07-04T11:52:11ZengSpringerOpenJournal of High Energy Physics1029-84792021-06-012021612710.1007/JHEP06(2021)171The structure of IR divergences in celestial gluon amplitudesHernán A. González0Francisco Rojas1Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo IbáñezFacultad de Ingeniería y Ciencias, Universidad Adolfo IbáñezAbstract 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 N $$ \mathcal{N} $$ = 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.https://doi.org/10.1007/JHEP06(2021)171Conformal Field TheoryScattering AmplitudesField Theories in Lower Dimensions |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Hernán A. González Francisco Rojas |
spellingShingle |
Hernán A. González Francisco Rojas The structure of IR divergences in celestial gluon amplitudes Journal of High Energy Physics Conformal Field Theory Scattering Amplitudes Field Theories in Lower Dimensions |
author_facet |
Hernán A. González Francisco Rojas |
author_sort |
Hernán A. González |
title |
The structure of IR divergences in celestial gluon amplitudes |
title_short |
The structure of IR divergences in celestial gluon amplitudes |
title_full |
The structure of IR divergences in celestial gluon amplitudes |
title_fullStr |
The structure of IR divergences in celestial gluon amplitudes |
title_full_unstemmed |
The structure of IR divergences in celestial gluon amplitudes |
title_sort |
structure of ir divergences in celestial gluon amplitudes |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2021-06-01 |
description |
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 N $$ \mathcal{N} $$ = 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. |
topic |
Conformal Field Theory Scattering Amplitudes Field Theories in Lower Dimensions |
url |
https://doi.org/10.1007/JHEP06(2021)171 |
work_keys_str_mv |
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1721319891689013248 |