Conformal blocks from celestial gluon amplitudes
01 May 2021-Journal of High Energy Physics (Springer Science and Business Media LLC)-Vol. 2021, Iss: 5, pp 170
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.
Citations
More filters
TL;DR: In this paper, the conformally soft charges can be expressed in terms of light ray integrals that select modes of the appropriate conformal weights, and they reside at the bottom corners of memory diamonds, and ascend to generalized currents.
Abstract: Celestial diamonds encode the structure of global conformal multiplets in 2D celestial CFT and offer a natural language for describing the conformally soft sector. The operators appearing at their left and right corners give rise to conformally soft factorization theorems, the bottom corners correspond to conserved charges, and the top corners to conformal dressings. We show that conformally soft charges can be expressed in terms of light ray integrals that select modes of the appropriate conformal weights. They reside at the bottom corners of memory diamonds, and ascend to generalized currents. We then identify the top corners of the associated Goldstone diamonds with conformal Faddeev-Kulish dressings and compute the sub-leading conformally soft dressings in gauge theory and gravity which are important for finding nontrivial central extensions. Finally, we combine these ingredients to speculate on 2D effective descriptions for the conformally soft sector of celestial CFT.
54 citations
TL;DR: In this paper, the structure of global conformal multiplets in 2D celestial CFT was examined and all the SL(2,ℂ) primary descendants were organized into celestial diamonds.
Abstract: We examine the structure of global conformal multiplets in 2D celestial CFT. For a 4D bulk theory containing massless particles of spin s = $$ \left\{0,\frac{1}{2},1,\frac{3}{2},2\right\} $$
we classify and construct all SL(2,ℂ) primary descendants which are organized into ‘celestial diamonds’. This explicit construction is achieved using a wavefunction-based approach that allows us to map 4D scattering amplitudes to celestial CFT correlators of operators with SL(2,ℂ) conformal dimension ∆ and spin J. Radiative conformal primary wavefunctions have J = ±s and give rise to conformally soft theorems for special values of ∆ ∈ $$ \frac{1}{2}\mathbb{Z} $$
. They are located either at the top of celestial diamonds, where they descend to trivial null primaries, or at the left and right corners, where they descend both to and from generalized conformal primary wavefunctions which have |J| ≤ s. Celestial diamonds naturally incorporate degeneracies of opposite helicity particles via the 2D shadow transform relating radiative primaries and account for the global and asymptotic symmetries in gauge theory and gravity.
48 citations
TL;DR: In this article, the bulk-to-boundary dictionary for 4D celestial holography is given a new entry defining 2D boundary states living on oriented circles on the celestial sphere, and the BPZ construction is applied to give an inner product on such states whose associated bulk adjoints are shown to involve a shadow transform.
Abstract: The bulk-to-boundary dictionary for 4D celestial holography is given a new entry defining 2D boundary states living on oriented circles on the celestial sphere. The states are constructed using the 2D CFT state-operator correspondence from operator insertions corresponding to either incoming or outgoing particles which cross the celestial sphere inside the circle. The BPZ construction is applied to give an inner product on such states whose associated bulk adjoints are shown to involve a shadow transform. Scattering amplitudes are then given by BPZ inner products between states living on the same circle but with opposite orientations. 2D boundary states are found to encode the same information as their 4D bulk counterparts, but organized in a radically different manner.
36 citations
24 Mar 2022
TL;DR: The soft limits of scattering amplitudes have been extensively studied due to their essential role in the computation of physical observables in collider physics, and the universal factorisation that occurs in these kinematic limits has been shown to be related to conservation laws associated with asymptotic, or large, gauge symmetries as mentioned in this paper .
Abstract: The soft limits of scattering amplitudes have been extensively studied due to their essential role in the computation of physical observables in collider physics. The universal factorisation that occurs in these kinematic limits has been shown to be related to conservation laws associated with asymptotic, or large, gauge symmetries. This connection has led to a deeper understanding of the symmetries of gauge and gravitational theories and to a reformulation of scattering amplitudes in a basis of boost eigenstates which makes manifest the two-dimensional global conformal symmetry of the celestial sphere. The recast, or celestial, amplitudes possess many of the properties of conformal field theory (CFT) correlation functions which has suggested a path towards a holographic description of asymptotically flat spacetimes. In this review we consider these interconnected developments in our understanding of soft theorems, asymptotic symmetries and CFT with a focus on the structure and symmetries of the celestial amplitudes and their holographic interpretation.
34 citations
TL;DR: In this paper, the authors adopt a procedure similar to minimal models and construct a single-valued completion of the shadow correlator, in the limit when the shadow is soft, which allows inverting the shadow transform and constructing a singlevalued celestial four-gluon amplitude.
Abstract: In a recent paper, here referred to as part I, we considered the celestial four-gluon amplitude with one gluon represented by the shadow transform of the corresponding primary field operator. This correlator is ill-defined because it contains branch points related to the presence of conformal blocks with complex spin. In this work, we adopt a procedure similar to minimal models and construct a single-valued completion of the shadow correlator, in the limit when the shadow is “soft.” By following the approach of Dotsenko and Fateev, we obtain an integral representation of such a single-valued correlator. This allows inverting the shadow transform and constructing a single-valued celestial four-gluon amplitude. This amplitude is drastically different from the original Mellin amplitude. It is defined over the entire complex plane and has correct crossing symmetry, OPE and bootstrap properties. It agrees with all known OPEs of celestial gluon operators. The conformal block spectrum consists of primary fields with dimensions ∆ = m + iλ, with integer m ≥ 1 and various, but always integer spin, in all group representations contained in the product of two adjoint representations.
30 citations
References
More filters
TL;DR: In this paper, it is shown that the flow of information to infinity is controlled by a single function of two variables called the news function, together with initial conditions specified on a light cone, which fully defines the behaviour of the system.
Abstract: This paper is divided into four parts. In part A, some general considerations about gravitational radiation are followed by a treatment of the scalar wave equation in the manner later to be applied to Einstein’s field equations. In part B, a co-ordinate system is specified which is suitable for investigation of outgoing gravitational waves from an isolated axi-symmetric reflexion-symmetric system . The metric is expanded in negative powers of a suitably defined radial co-ordinate r , and the vacuum field equations are investigated in detail. It is shown that the flow of information to infinity is controlled by a single function of two variables called the news function. Together with initial conditions specified on a light cone, this function fully defines the behaviour of the system . No constraints of any kind are encountered. In part C, the transformations leaving the metric in the chosen form are determined. An investigation of the corresponding transformations in Minkowski space suggests that no generality is lost by assuming that the transformations, like the metric, may be expanded in negative powers of r . In part D, the mass of the system is defined in a way which in static metrics agrees with the usual definition. The principal result of the paper is then deduced, namely, that the mass of a system is constant if and only if there is no news; if there is news, the mass decreases monotonically so long as it continues. The linear approximation is next discussed, chiefly for its heuristic value, and employed in the analysis of a receiver for gravitational waves. Sandwich waves are constructed, and certain non-radiative but non-static solutions are discussed. This part concludes with a tentative classification of time-dependent solutions of the types considered.
2,324 citations
TL;DR: In this paper, a convenient way of splitting the metric tensor and the Einstein field equations, applicable in any space-time, is first introduced, and suitable boundary conditions are set.
Abstract: Gravitational fields containing bounded sources and gravitational radiation are examined by analyzing their properties at spatial infinity. A convenient way of splitting the metric tensor and the Einstein field equations, applicable in any space-time, is first introduced. Then suitable boundary conditions are set. The group of co-ordinate transformations that preserves the boundary conditions is analyzed. Different possible gravitational fields are characterized intrinsically by a combination of (i) characteristic initial data, and (ii) Dirichlet data at spatial infinity. To determine a particular solution one must specify four functions of three variables and three functions of two variables; these functions are not subject to constraints. A method for integrating the field equations is given; the asymptotic behaviour of the metric and Riemann tensors for large spatial distances is analyzed in detail; the dynamical variables of the radiation modes are exhibited; and a superposition principle for the radiation modes of the gravitational field is suggested. Among the results are: (i) the group of allowed co-ordinate transformations contains the inhomogeneous orthochronous Lorentz group as a subgroup; (ii) each of the five leading terms in an asymptotic expansion of the Riemann tensor has the algebraic structure previously predicted from analyzing the Petrov classification; (iii) gravitational waves appear to carry mass away from the interior; (iv) time-dependent periodic solutions of the field equations which obey the stated boundary conditions do not exist. It was found that the general fields studied in the present work are in many ways very similar to the axially symmetric fields recently studied by Bondi, van der Burg & Metzner.
1,716 citations
TL;DR: In this paper, it was shown that the divergence arising in the quantum theory of gravitation can be removed by the familiar methods used in quantum electrodynamics, and it was proved that for infrared gravitons this divergence cancels in the sum of all such diagrams.
Abstract: It is shown that the infrared divergences arising in the quantum theory of gravitation can be removed by the familiar methods used in quantum electrodynamics. An additional divergence appears when infrared photons or gravitons are emitted from noninfrared external lines of zero mass, but it is proved that for infrared gravitons this divergence cancels in the sum of all such diagrams. (The cancellation does not occur in massless electrodynamics.) The formula derived for graviton bremsstrahlung is then used to estimate the gravitational radiation emitted during thermal collisions in the sun, and we find this to be a stronger source of gravitational radiation (though still very weak) than classical sources such as planetary motion. We also verify the conjecture of Dalitz that divergences in the Coulomb-scattering Born series may be summed to an innocuous phase factor, and we show how this result may be extended to processes involving arbitrary numbers of relativistic or nonrelativistic particles with arbitrary spin.
1,253 citations
TL;DR: In this paper, the results of Christodoulou and Klainerman were applied within a suitable finite neighborhood of the Minkowski vacuum to identify diagonal elements BMS0 of BMS+ × BMS−.
Abstract: BMS+ transformations act nontrivially on outgoing gravitational scattering data while preserving intrinsic structure at future null infinity (
$$ \mathrm{\mathcal{I}} $$
+). BMS− transformations similarly act on ingoing data at past null infinity (
$$ \mathrm{\mathcal{I}} $$
−). In this paper we apply — within a suitable finite neighborhood of the Minkowski vacuum — results of Christodoulou and Klainerman to link $$ \mathrm{\mathcal{I}} $$
+ to $$ \mathrm{\mathcal{I}} $$
− and thereby identify “diagonal” elements BMS0 of BMS+ × BMS−. We argue that BMS0 is a nontrivial infinite-dimensional symmetry of both classical gravitational scattering and the quantum gravity $$ \mathcal{S} $$
-matrix. It implies the conservation of net accumulated energy flux at every angle on the conformal S
2 at $$ \mathrm{\mathcal{I}} $$
. The associated Ward identity is shown to relate S-matrix elements with and without soft gravitons. Finally, BMS0 is recast as a U(1) Kac-Moody symmetry and an expression for the Kac-Moody current is given in terms of a certain soft graviton operator on the boundary of $$ \mathrm{\mathcal{I}} $$
.
841 citations
TL;DR: In this article, it was conjectured that a certain infinite-dimensional subgroup of BMS supertranslations acting on past and future null infinity is an exact symmetry of the quantum gravity S-matrix, and an associated Ward identity was derived.
Abstract: Recently it was conjectured that a certain infinite-dimensional “diagonal” subgroup of BMS supertranslations acting on past and future null infinity (
and ) is an exact symmetry of the quantum gravity S-matrix, and an associated Ward identity was derived. In this paper we show that this supertranslation Ward identity is precisely equivalent to Weinberg’s soft graviton theorem. Along the way we construct the canonical generators of supertranslations at , including the relevant soft graviton contributions. Boundary conditions at the past and future of and a correspondingly modified Dirac bracket are required. The soft gravitons enter as boundary modes and are manifestly the Goldstone bosons of spontaneously broken supertranslation invariance.
712 citations