On Sugawara construction on celestial sphere

Section: Jhep06(2021)079mentioning

confidence: 99%

Coadjoint representation of the BMS group on celestial Riemann surfaces

Barnich

Ruzziconi

2021

“…Therefore, since the energies ω * i do transform under SL(2,C), one may wonder whether the explicit dependence on the ω * i in the expression for h 5 in (2.43) could spoil the aforementioned covariance. The answer is of course not, since from (2.41) and the explicit expressions for f ij (see appendix A of [46]) one notices that they transform in such a way that the final evaluated expression for h 5 ({ω * i }, ω 5 ) ends up being conformal invariant. After evaluating h 5 ({ω * i }, ω 5 ) one obtains…”

Section: Jhep06(2021)171mentioning

confidence: 99%

The structure of IR divergences in celestial gluon amplitudes

González

Rojas

2021

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 $$ \mathcal{N} $$ 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.

“…This construction resembles the Sugawara construction of the energy momentum tensor for affine Lie algebras. See[37] for a recent discussion, where it was shown that the energy momentum tensor and supertranslation current[11] can be constructed as composite operators of conformally soft gluon states.…”

mentioning

confidence: 99%

Extended super BMS algebra of celestial CFT

Fotopoulos

Stieberger

Taylor

et al. 2020

Self Cite

134

We study two-dimensional celestial conformal field theory describing four- dimensional $$ \mathcal{N} $$ N =1 supergravity/Yang-Mills systems and show that the underlying symmetry is a supersymmetric generalization of BMS symmetry. We construct fermionic conformal primary wave functions and show how they are related via supersymmetry to their bosonic partners. We use soft and collinear theorems of supersymmetric Einstein-Yang- Mills theory to derive the OPEs of the operators associated to massless particles. The bosonic and fermionic soft theorems are shown to form a sequence under supersymmetric Ward identities. In analogy with the energy momentum tensor, the supercurrents are shadow transforms of soft gravitino operators and generate an infinite-dimensional super- symmetry algebra. The algebra of $$ {\mathfrak{sbms}}_4 $$ sbms 4 generators agrees with the expectations based on earlier work on the asymptotic symmetry group of supergravity. We also show that the supertranslation operator can be written as a product of holomorphic and anti-holomorphic supercurrents.