Descendants in celestial CFT and emergent multi-collinear factorization

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.

Section: Jhep05(2021)282mentioning

confidence: 99%

“…In order to clarify the correspondence, let us begin by giving a precise definition of the collinear limit (see also ref. [65]). Following standard practices in QCD, in order to describe the situation in which two light-like momenta p 1 and p 2 become collinear along a light-like direction p, we introduce the Sudakov parametrisation…”

Section: Jhep05(2021)282mentioning

confidence: 99%

Non-abelian infrared divergences on the celestial sphere

Magnea

2021

“…The leading graviton theorem is related to supertranslations which together with superrotations generate the algebra of BMS symmetry [19]. Another important component are collinear theorems [20] which allow studying the limits of operator insertions at coinciding points, hence deriving the operator product expansions of the operators associated to gluons and gravitons [13,19,[21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Conformal blocks from celestial gluon amplitudes

Fan

Fotopoulos

Stieberger

et al. 2021

In celestial conformal field theory, gluons are represented by primary fields with dimensions ∆ = 1 + iλ, λ ∈ ℝ and spin J = ±1, in the adjoint representation of the gauge group. All two- and three-point correlation functions of these fields are zero as a consequence of four-dimensional kinematic constraints. Four-point correlation functions contain delta-function singularities enforcing planarity of four-particle scattering events. We relax these constraints by taking a shadow transform of one field and perform conformal block decomposition of the corresponding correlators. We compute the conformal block coefficients. When decomposed in channels that are “compatible” in two and four dimensions, such four-point correlators contain conformal blocks of primary fields with dimensions ∆ = 2 + M + iλ, where M ≥ 0 is an integer, with integer spin J = −M, −M + 2, …, M − 2, M. They appear in all gauge group representations obtained from a tensor product of two adjoint representations. When decomposed in incompatible channels, they also contain primary fields with continuous complex spin, but with positive integer dimensions.

“…So a natural question arises as to how the bulk scattering amplitudes in four dimensions are constrained by the infinite dimensional symmetries of the dual CCFT. For recent developments in this direction please see [3][4][5][6][7][8][9].…”

Section: Jhep10(2021)111 1 Introductionmentioning

confidence: 99%

MHV gluon scattering amplitudes from celestial current algebras

Banerjee

Ghosh

2021

We show that the Mellin transform of an n-point tree level MHV gluon scattering amplitude, also known as the celestial amplitude in pure Yang-Mills theory, satisfies a system of (n−2) linear first order partial differential equations corresponding to (n−2) positive helicity gluons. Although these equations closely resemble Knizhnik-Zamoldochikov equations for SU(N) current algebra there is also an additional “correction” term coming from the subleading soft gluon current algebra. These equations can be used to compute the leading term in the gluon-gluon OPE on the celestial sphere. Similar equations can also be written down for the momentum space tree level MHV scattering amplitudes. We also propose a way to deal with the non closure of subleading current algebra generators under commutation. This is then used to compute some subleading terms in the mixed helicity gluon OPE.