Double-soft graviton amplitudes and the extended BMS charge algebra

The basic ingredient of CCFT holography is to regard four-dimensional amplitudes describing conformal wave packets as two-dimensional conformal correlation functions of the operators associated to external particles. By construction, these operators transform as quasi-primary fields under SL(2, C) conformal symmetry group of the celestial sphere. We derive the OPE of the CCFT energy-momentum tensor with the operators representing gauge bosons and show that they transform as Virasoro primaries under diffeomorphisms of the celestial sphere.

“…This OPE has already been discussed in the context of doublesoft limits in Ref. [25]. In our approach, it should emerge from the collinear limit of two shadow operators.…”

Section: Discussionmentioning

confidence: 78%

Primary fields in celestial CFT

Fotopoulos

Taylor

2019

“…Another important point is that the BMS algebra may have (field-dependent) central extension [46,47]. In this paper the central extension does not play any role because in the first subleading order the Virasoro descendants {L −n φ, n > 1} do not appear, although they appear in the higher order of the OPE.…”

Section: Future Directionsmentioning

confidence: 90%

BMS symmetry of celestial OPE

Banerjee

Ghosh

Gonzo

2020

106

103

In this paper we study the BMS symmetry of the celestial OPE of two positive helicity gravitons in Einstein theory in four dimensions. The celestial OPE is obtained by Mellin transforming the scattering amplitude in the (holomorphic) collinear limit. The collinear limit at leading order gives the singular term of the celestial OPE. We compute the first subleading correction to the OPE by analysing the four graviton scattering amplitude directly in Mellin space. The subleading term can be written as a linear combination of BMS descendants with the OPE coefficients determined by BMS algebra and the coefficient of the leading term in the OPE. This can be done by defining a suitable BMS primary state. We find that among the descendants, which appear at the first subleading order, there is one which is created by holomorphic supertranslation with simple pole on the celestial sphere.

“…Applying the results of appendix A to equation (20), one obtains the renormalized normal-component to the hypersurface Ω = const. ≥ 0 in the form 9…”

Section: Renormalizing the Symplectic Potentialmentioning

confidence: 99%

“…2ℓ+1) = 0 do not determine the Maxwell news and the charge aspect, they of course still hold true. Similarly to the SP radial equation (20) which is controlled by the logarithmic anomaly C of equation (27), the E A and E u equations for J A and J u are also controlled by their own logarithmic anomalies. We will call them the vector and scalar anomaly respectively.…”

Section: Anomaliesmentioning

confidence: 99%

“…These are naturally part of the algebra at finite boundaries [13], but are excluded in the standard construction of the asymptotic symmetries of gravity which only features the BMS group (see [14] for an enlightening review, and references therein). In recent years, two different attempts at including super-rotations in the asymptotic symmetry structure have been made [15][16][17][18] (see also [19,20] for the connection to the subleading soft graviton theorems). However, serious challenges in the definition of the super-rotation charges emerge [12,21].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotic renormalization in flat space: symplectic potential and charges of electromagnetism

Freidel

Hopfmüller

Riello

2019

We present a systematic procedure to renormalize the symplectic potential of the electromagnetic field at null infinity in Minkowski space. We work in D ≥ 6 spacetime dimensions as a toy model of General Relativity in D ≥ 4 dimensions. Total variation counterterms as well as corner counterterms are both subtracted from the symplectic potential to make it finite. These counterterms affect respectively the action functional and the Hamiltonian symmetry generators. The counterterms are local and universal. We analyze the asymptotic equations of motion and identify the free data associated with the renormalized canonical structure along a null characteristic. This allows the construction of the asymptotic renormalized charges whose Ward identity gives the QED soft theorem, supporting the physical viability of the renormalization procedure. We touch upon how to extend our analysis to the presence of logarithmic anomalies, and upon how our procedure compares to holographic renormalization. * lfreidel@perimeterinstitute.ca † fhopfmueller@perimeterinstitute.ca ‡ ariello@perimeterinstitute.ca