Abstract
Celestial holography promisingly reformulates the scattering amplitude holographically in terms of celestial conformal field theory living at null infinity. Recently, an infinite-dimensional symmetry algebra was discovered in Einstein-Yang-Mills theory. The starting point in the derivation is the celestial OPE of two soft currents, and the key ingredient is the summation of overline{mathrm{SL}left(2,mathbb{R}right)} descendants in OPE. In this paper, we consider the supersymmetric Einstein-Yang-Mills theory and obtain the supersymmetric extension of the holographic symmetry algebra. Furthermore, we derive infinitely many Ward identities associated with the infinite soft currents which generate the holographic symmetry algebra. This is realized by considering the OPE between a soft symmetry current and a hard operator, and then summing over its overline{mathrm{SL}left(2,mathbb{R}right)} descendants. These Ward identities reproduce the known Ward identities corresponding to the leading, sub-leading, and sub-sub-leading soft graviton theorems as well as the leading and sub-leading soft gluon theorems. By performing shadow transformations, we also obtain infinitely many shadow Ward identities, including the stress tensor Ward identities for sub-leading soft graviton. Finally, we use our procedure to discuss the corrections to Ward identities in effective field theory (EFT), and reproduce the corrections to soft theorems at sub-sub-leading order for graviton and sub-leading order for photon. For this aim, we derive general formulae for the celestial OPE and its corresponding Ward identities arising from a cubic interaction of three spinning massless particles. Our formalism thus provides a unified framework for understanding the Ward identities in celestial conformal field theory, or equivalently the soft theorems in scattering amplitude.
Highlights
Symmetry is arguably one of the most important guiding principles in physics
Celestial holography promisingly reformulates the scattering amplitude holographically in terms of celestial conformal field theory living at null infinity
While for the holographic chiral algebra itself, we show that it is robust and free from corrections in effective field theory (EFT), on condition that we consider the case with only positive helicity soft particles where our formalism applies
Summary
Symmetry is arguably one of the most important guiding principles in physics. The content and power of symmetry have always been evolving with time. The important ingredient in their derivation is that one needs to sum over all the SL(2, R) descendants in OPEs. Taking soft limits for both positive helicity operators, which is unambiguous in this case, and decomposing the resulting soft currents into chiral currents, they obtain the desired algebra of these infinitely many chiral currents. We will consider the supersymmetric Einstein-Yang-Mills theory and derive the corresponding holographic symmetry algebra by summing over the SL(2, R) descendants of two soft currents. While for the holographic chiral algebra itself, we show that it is robust and free from corrections in EFT, on condition that we consider the case with only positive helicity soft particles where our formalism applies. While we were completing the paper, we learned that the new paper [19] obtained the celestial OPEs for arbitrary spinning operators, which is derived in our appendix C and subsection 6.1
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