Descendants in celestial CFT and emergent multi-collinear factorization
02 Mar 2021-Journal of High Energy Physics (Springer Science and Business Media LLC)-Vol. 2021, Iss: 3, pp 1-27
TL;DR: In this article, a systematic study of conformal and Kac-Moody descendants in the OPE of celestial gluons was conducted, and the results of these OPEs were used for computing the multi-collinear limits of gluon amplitudes.
Abstract: Multi-collinear factorization limits provide a window to study how locality and unitarity of scattering amplitudes can emerge dynamically from celestial CFT, the conjectured holographic dual to gauge and gravitational theories in flat space. To this end, we first use asymptotic symmetries to commence a systematic study of conformal and Kac-Moody descendants in the OPE of celestial gluons. Recursive application of these OPEs then equips us with a novel holographic method of computing the multi-collinear limits of gluon amplitudes. We perform this computation for some of the simplest helicity assignments of the collinear particles. The prediction from the OPE matches with Mellin transforms of the expressions in the literature to all orders in conformal descendants. In a similar vein, we conclude by studying multi-collinear limits of graviton amplitudes in the leading approximation of sequential double-collinear limits, again finding a consistency check against the leading order OPE of celestial gravitons.
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TL;DR: In this article, the authors construct two towers of 2D currents from positive-helicity photons, gluons, or gravitons with integer conformal weights, which generate the symmetries associated to an infinite tower of conformally soft theorems.
Abstract: All 4D gauge and gravitational theories in asymptotically flat spacetimes contain an infinite number of non-trivial symmetries. They can be succinctly characterized by generalized 2D currents acting on the celestial sphere. A complete classification of these symmetries and their algebras is an open problem. Here we construct two towers of such 2D currents from positive-helicity photons, gluons, or gravitons with integer conformal weights. These generate the symmetries associated to an infinite tower of conformally soft theorems. The current algebra commutators are explicitly derived from the poles in the OPE coefficients, and found to comprise a rich closed subalgebra of the complete symmetry algebra.
144 citations
TL;DR: In this paper, a shadow transform of one field is decomposed 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.
Abstract: 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.
63 citations
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TL;DR: In this paper, 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 linear first order partial differential equations corresponding to positive helicity gluons.
Abstract: 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-Zamolodchikov 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 and our results match with those obtained from an explicit calculation using the Mellin MHV amplitude.
45 citations
TL;DR: In this paper, the form of the universal color operator responsible for infrared divergences, when expressed in terms of coordinates on the "celestial sphere" intersecting the future light-cone at asymptotic distances, was studied.
Abstract: 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.
30 citations
TL;DR: In this paper, 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 linear first order partial differential equations corresponding to (n−2) positive helicity gluons.
Abstract: 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.
28 citations
References
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TL;DR: In this article, the main body of predictions of the theory for deep-inleastic scattering on either unpolarized or polarized targets is re-obtained by a method which only makes use of the simplest tree diagrams and is entirely phrased in parton language with no reference to the conventional operator formalism.
4,692 citations
TL;DR: A short and direct proof of this recursion relation for tree-level scattering amplitudes based on properties of tree- level amplitudes only is given.
Abstract: Recently, by using the known structure of one-loop scattering amplitudes for gluons in Yang-Mills theory, a recursion relation for tree-level scattering amplitudes has been deduced. Here, we give a short and direct proof of this recursion relation based on properties of tree-level amplitudes only.
1,605 citations
TL;DR: In this article, the authors presented new recursion relations for tree amplitudes in gauge theory that give very compact formulas, in which all particles are on-shell and momentum conservation is preserved.
1,267 citations
29 Sep 2014
TL;DR: In this article, the authors present a concise review of developments on various continuous multivariate distributions and present some basic definitions and notations, and present several important continuous multi-dimensional distributions and their significant properties and characteristics.
Abstract: In this article, we present a concise review of developments on various continuous multivariate distributions. We first present some basic definitions and notations. Then, we present several important continuous multivariate distributions and list their significant properties and characteristics.
Keywords:
generating function;
moments;
conditional distribution;
truncated distribution;
regression;
bivariate normal;
multivariate normal;
multivariate exponential;
multivariate gamma;
dirichlet;
inverted dirichlet;
liouville;
multivariate logistic;
multivariate pareto;
multivariate extreme value;
multivariate t;
wishart translated systems;
multivariate exponential families
1,106 citations
"Descendants in celestial CFT and em..." refers background in this paper
...where the integral can be performed by noticing that the integrand is an example of a generalized Dirichlet distribution ([44], chapter 49)....
[...]
..., an) = Γ(a1) · · ·Γ(an)/Γ(a1+· · ·+an) is the multivariate beta function, and the integral has been performed by recognizing that its integrand is a standard Dirichlet distribution ([44], chapter 49)....
[...]
28 Jan 2005
990 citations