Abstract
Conformally soft gluons are conserved currents of the Celestial Conformal Field Theory (CCFT) and generate a Kac-Moody algebra. We study celestial amplitudes of Yang-Mills 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 energy-momentum tensor of the CCFT. We verify that conformally soft gauge bosons are Virasoro primaries of the CCFT under the Sugawara energy-momentum tensor. The Sugawara tensor though does not generate the correct conformal transformations for hard states. In Einstein-Yang- Mills theory, we consider an alternative construction of the energy-momentum 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.
Highlights
Correlators on the celestial conformal field theory (CCFT)
The study of Celestial Conformal Field Theory (CCFT) and its properties has led to several advances along various aspects of the proposed theory [4, 7, 16,17,18,19,20,21,22,23,24,25,26], but a lot remains in order to make the CCFT a solid proposal for flat space-time holography
In CCFT, each particle corresponds to a conformal field operator with Re(∆) = 1, i.e. ∆ = 1 + iλ, λ ∈ R [2]
Summary
Taking the consecutive double soft limit ∆1, ∆2 → 1 of the mixed helicity gluon OPE we see that the result depends on the order of limits. In this paper we will construct the Sugawara energy momentum tensor using the double conformal soft limit of celestial amplitudes like (2.8). We will consider gluon amplitudes and study the limit where the Sugawara tensor becomes collinear with conformally soft positive helicity gluons, the holomorphic current algebra currents ja(z). From the CCFT theory point of view the Sugawara construction (2.22) corresponds to performing the double conformal soft limit of two positive helicity gluons taken to be collinear at the same time. We shall construct the Sugawara energy-momentum T S(z) and derive its OPE with conserved currents j(z) in the celestial amplitude (2.8) In the latter we use the conformal primary operators. The only difference is in the single pole term, where the numerator z142 would modify the derivative term of (3.11) as (3.3)
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