Loop corrections to celestial amplitudes

The gravitational charge algebra of generic asymptotically locally (A)dS spacetimes is derived in n dimensions. The analysis is performed in the Starobinsky/Fefferman-Graham gauge, without assuming any further boundary condition than the minimal falloffs for conformal compactification. In particular, the boundary structure is allowed to fluctuate and plays the role of source yielding some symplectic flux at the boundary. Using the holographic renormalization procedure, the divergences are removed from the symplectic structure, which leads to finite expressions. The charges associated with boundary diffeomorphisms are generically non-vanishing, non-integrable and not conserved, while those associated with boundary Weyl rescalings are non-vanishing only in odd dimensions due to the presence of Weyl anomalies in the dual theory. The charge algebra exhibits a field-dependent 2-cocycle in odd dimensions. When the general framework is restricted to three-dimensional asymptotically AdS spacetimes with Dirichlet boundary conditions, the 2-cocycle reduces to the Brown-Henneaux central extension. The analysis is also specified to leaky boundary conditions in asymptotically locally (A)dS spacetimes that lead to the Λ-BMS asymptotic symmetry group. In the flat limit, the latter contracts into the BMS group in n dimensions.

Section: Jhep05(2021)210 6 Commentsmentioning

confidence: 99%

Charge algebra in Al(A)dSn spacetimes

Fiorucci

Ruzziconi

2021

“…At the moment, much of the work done within this framework is focused on tree-level amplitudes for gauge theories and gravity (see, however, refs. [53,54], where one-loop effects are analysed), but the connection that has been uncovered between infrared properties of d = 4 massless field theories and d = 2 conformal invariance on the celestial sphere is intriguing, and represents a radically innovative point of view on an old problem. An important new tool introduced in this context has been the use of Mellin transforms of scattering amplitudes [55,56], which are constructed to have simple transformation properties under the conformal group acting on the celestial sphere, while from a four-dimensional viewpoint they are boost eigenstates.…”

Section: Jhep05(2021)282mentioning

confidence: 99%

Non-abelian infrared divergences on the celestial sphere

Magnea

2021

We consider the infrared factorisation of non-abelian multi-particle scattering amplitudes, and we study the form of the universal colour operator responsible for infrared divergences, when expressed in terms of coordinates on the ‘celestial sphere’ intersecting the future light-cone at asymptotic distances. We find that colour-dipole contributions to the infrared operator, to all orders in perturbation theory, have a remarkably simple expression in these coordinates, with scale and coupling dependence factorised from kinematics and colour. Generalising earlier suggestions in the abelian theory, we then show that the infrared operator can be computed as a correlator of vertex operators in a conformal field theory of Lie-algebra-valued free bosons on the celestial sphere. We verify by means of the OPE that the theory correctly predicts the all-order structure of collinear limits, and the tree-level factorisation of soft real radiation.

“…For certain classes of celestial amplitudes in four dimensions all-multiplicity formulas already exist in the literature: tree-level Yang-Mills MHV and NMHV amplitudes were computed in [18]. These computations are done by performing Mellin transforms on the energies of the external particles which, while doable for some low point amplitudes including loop [16,19] and string [20] amplitudes, become highly involved for generic amplitudes. CFT inspired methods have also been used to holographically constrain MHV amplitudes [21,22] and it might be that further understanding of the celestial OPEs [13,[23][24][25] will lead to better methods.…”

Section: Jhep05(2021)157mentioning

confidence: 99%

“…It would be interesting to see if there is a way to encode the effect of loop momentum in the numerators in terms of operators acting on the external variables. Perhaps, some insight could be gained from explicit Mellin transforms giving loop-level celestial amplitudes [16,19,79].…”

Section: Jhep05(2021)157mentioning

confidence: 99%

“…This has the effect of mixing the UV and the IR. Yet universal properties of amplitudes, such as soft limits and IR factorization [1,[5][6][7][8][9][10][11][12][13][14][15][16], survive this change of basis albeit in a different guise. Recently, it was shown in [17] that relations between the S-matrices of Yang-Mills and gravity known as the double copy also survives this change of basis, at least up to four point amplitudes.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Celestial double copy from the worldsheet

Casali

Sharma

2021

Using the ambitwistor string, we compute tree-level celestial amplitudes for biadjoint scalars, Yang-Mills and gravity to all multiplicities. They are presented in compact CHY-like formulas with operator-valued scattering equations and numerators acting on a generalized hypergeometric function. With these we extend the celestial double copy to tree-level amplitudes with arbitrary number of external states. We also show how color-kinematics duality is implemented in celestial amplitudes and its interpretation in terms of a generalized twisted cohomology theory.