Soft gravity by squaring soft QED on the celestial sphere

Nikhil Kalyanapuram

doi:10.1103/physrevd.103.085016

Nikhil Kalyanapuram

Open Access

https://doi.org/10.1103/physrevd.103.085016

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Abstract

We recast the soft $S$-matrices on the celestial sphere as correlation functions of certain $2$-dimensional models of topological defects. In pointing out the double copy structure between the soft photon and soft graviton cases, we arrive at a putative classical double copy between the corresponding topological models and a rederivation of gauge invariance and the equivalence principle as Ward identities of the $2$-dimensional theories.

Highlights

The study of scattering amplitudes as analytical objects in their own right has been a rather fertile one in recent years
Of particular interest has been the soft sector of the S matrix for theories with massless particles, which as it turns out reflects underlying symmetries which are manifest at null infinity
Emerging from this analysis is a picture of flat space holography, in which particles on the celestial sphere control most of the analytic properties of the entire S matrix

Summary

INTRODUCTION

The study of scattering amplitudes as analytical objects in their own right has been a rather fertile one in recent years. The representation of the S matrix in terms of operators on the celestial sphere is realized by a change of basis brought about by the Mellin transform [23,24] In this basis, the infrared sector of the S matrix can be understood with relative ease in terms of operator product expansions of insertions on CP1 [25,26,27,28]. The infrared sector of the S matrix can be understood with relative ease in terms of operator product expansions of insertions on CP1 [25,26,27,28] This has led to a conjectural 4d=2d duality, which relates the S matrix to correlation functions of operators of an alleged conformal field theory (CFT) on the celestial sphere. While dualities are normally meant to express equivalences between strongly and weakly coupled theories, the dualities we discuss are all between weakly coupled theories

A DUALITY ON THE CELESTIAL SPHERE

A DOUBLE COPY ON THE CELESTIAL SPHERE

THE SOFT THEOREMS

DISCUSSION