We propose a description of the gluon scattering amplitudes as the inverse Mellin transforms of the conformal correlators of light operators in twodimensional Liouville theory tensored with WZWlike chiral currents on the celestial sphere. The dimensions of operators are Mellin dual to gluon light cone energies while their positions are determined by the gluon momentum directions. Treelevel approximation in YangMills theory corresponds to the semiclassical limit of Liouville theory. By comparing subleading corrections, we find b^2=(8π^2)^{−1}b_0g^2(M), where b is the Liouville coupling constant, g(M) is the Yang Mills coupling at the renormalization scale M and b_0 is the oneloop coefficient of the YangMills beta function.
more »
« less
Elements of celestial conformal field theory
A bstract In celestial holography, fourdimensional scattering amplitudes are considered as twodimensional conformal correlators of a putative twodimensional celestial conformal field theory (CCFT). The simplest way of converting momentum space amplitudes into CCFT correlators is by taking their Mellin transforms with respect to lightcone energies. For massless particles, like gluons, however, such a construction leads to threepoint and fourpoint correlators that vanish everywhere except for a measure zero hypersurface of celestial coordinates. This is due to the fourdimensional momentum conservation law that constrains the insertion points of the operators associated with massless particles. These correlators are reminiscent of Coulomb gas correlators that, in the absence of background charges, vanish due to charge conservation. We supply the background momentum by coupling YangMills theory to a background dilaton field, with the (complex) dilaton source localized on the celestial sphere. This picture emerges from the physical interpretation of the solutions of the system of differential equations discovered by Banerjee and Ghosh. We show that the solutions can be written as Mellin transforms of the amplitudes evaluated in such a dilaton background. The resultant threegluon and fourgluon amplitudes are singlevalued functions of celestial coordinates enjoying crossing symmetry and all other properties expected from standard CFT correlators. We use them to extract OPEs and compare them with the OPEs extracted from multigluon celestial amplitudes without a dilaton background. We perform the conformal block decomposition of the fourgluon singlevalued correlator and determine the dimensions, spin and group representations of the entire primary field spectrum of the YangMills sector of CCFT.
more »
« less
 NSFPAR ID:
 10432152
 Date Published:
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2022
 Issue:
 8
 ISSN:
 10298479
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this


null (Ed.)A bstract Conformally soft gluons are conserved currents of the Celestial Conformal Field Theory (CCFT) and generate a KacMoody algebra. We study celestial amplitudes of YangMills 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 energymomentum tensor of the CCFT. We verify that conformally soft gauge bosons are Virasoro primaries of the CCFT under the Sugawara energymomentum tensor. The Sugawara tensor though does not generate the correct conformal transformations for hard states. In EinsteinYang Mills theory, we consider an alternative construction of the energymomentum 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.more » « less

null (Ed.)A bstract We study twodimensional celestial conformal field theory describing four dimensional $$ \mathcal{N} $$ N =1 supergravity/YangMills 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 EinsteinYang 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 infinitedimensional 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 antiholomorphic supercurrents.more » « less

null (Ed.)A bstract Multicollinear 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 KacMoody descendants in the OPE of celestial gluons. Recursive application of these OPEs then equips us with a novel holographic method of computing the multicollinear 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 multicollinear limits of graviton amplitudes in the leading approximation of sequential doublecollinear limits, again finding a consistency check against the leading order OPE of celestial gravitons.more » « less

A bstract In a recent paper, here referred to as part I, we considered the celestial fourgluon amplitude with one gluon represented by the shadow transform of the corresponding primary field operator. This correlator is illdefined 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 singlevalued 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 singlevalued correlator. This allows inverting the shadow transform and constructing a singlevalued celestial fourgluon 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.more » « less