BMS symmetry of celestial OPE

Conformally soft gluons are conserved currents of the Celestial Conformal Field Theory (CCFT) and generate a Kac-Moody algebra. We study celestial amplitudes of Yang-Mills theory, which are Mellin transforms of gluon amplitudes and take the double soft limit of a pair of gluons. In this manner we construct the Sugawara energy-momentum tensor of the CCFT. We verify that conformally soft gauge bosons are Virasoro primaries of the CCFT under the Sugawara energy-momentum tensor. The Sugawara tensor though does not generate the correct conformal transformations for hard states. In Einstein-Yang- Mills theory, we consider an alternative construction of the energy-momentum tensor, similar to the double copy construction which relates gauge theory amplitudes with gravity ones. This energy momentum tensor has the correct properties to generate conformal transformations for both soft and hard states. We extend this construction to supertranslations.

“…Any operator with ∆ = 1, (λ = 0) is called a hard operator for the purposes of this work 3. A study of representations of the BMS algebra on CS 2 was initiated in[37].…”

mentioning

confidence: 99%

On Sugawara construction on celestial sphere

Fan

Fotopoulos

Stieberger

et al. 2020

“…theorems familiar from Minkowski space amplitudes correspond to so called conformal soft theorems for celestial amplitudes, which were studied in [22][23][24][25][26][27][28][29][30]. The representation of BMS symmetry generators on the celestial sphere, and other aspects such as OPE expansions of celestial operators were discussed in [31][32][33][37][38][39][40]. Information contained at past boundary of future null infinity concerning local excitations in an asymptotically flat bulk space-time has been investigated in [34].…”

Section: Jhep11(2020)149mentioning

confidence: 99%

Relativistic partial waves for celestial amplitudes

Law

Zlotnikov

2020

The formalism of relativistic partial wave expansion is developed for four-point celestial amplitudes of massless external particles. In particular, relativistic partial waves are found as eigenfunctions to the product representation of celestial Poincaré Casimir operators with appropriate eigenvalues. The requirement of hermiticity of Casimir operators is used to fix the corresponding integral inner product, and orthogonality of the obtained relativistic partial waves is verified explicitly. The completeness relation, as well as the relativistic partial wave expansion follow. Example celestial amplitudes of scalars, gluons, gravitons and open superstring gluons are expanded on the basis of relativistic partial waves for demonstration. A connection with the formulation of relativistic partial waves in the bulk of Minkowski space is made in appendices.

“…On the one hand, the subleading soft graviton mode is a natural stress tensor candidate [14] for a putative dual celestial CFT with a Virasoro symmetry. This provoked reexamining scattering amplitudes in a basis [15][16][17] that makes conformal covariance manifest which, in turn, demanded a new understanding of the conformal analog of soft theorems [18][19][20][21][22][23][24][25][26][27]. While the leading conformally soft graviton naturally arises as the zero mode in this discussion, a puzzling question arose on how the subleading conformally soft graviton would fit into the appropriate conformal basis for celestial amplitudes.…”

Section: Jhep09(2020)176 Introductionmentioning

confidence: 99%

Asymptotic symmetries and celestial CFT

Donnay

Pasterski²,

Puhm

2020

151

227

We provide a unified treatment of conformally soft Goldstone modes which arise when spin-one or spin-two conformal primary wavefunctions become pure gauge for certain integer values of the conformal dimension ∆. This effort lands us at the crossroads of two ongoing debates about what the appropriate conformal basis for celestial CFT is and what the asymptotic symmetry group of Einstein gravity at null infinity should be. Finite energy wavefunctions are captured by the principal continuous series ∆ ∈ 1 + iℝ and form a complete basis. We show that conformal primaries with analytically continued conformal dimension can be understood as certain contour integrals on the principal series. This clarifies how conformally soft Goldstone modes fit in but do not augment this basis. Conformally soft gravitons of dimension two and zero which are related by a shadow transform are shown to generate superrotations and non-meromorphic diffeomorphisms of the celestial sphere which we refer to as shadow superrotations. This dovetails the Virasoro and Diff(S2) asymptotic symmetry proposals and puts on equal footing the discussion of their associated soft charges, which correspond to the stress tensor and its shadow in the two-dimensional celestial CFT.