On Carrollian Loop Amplitudes for Gauge Theory and Gravity

TL;DR

This paper investigates loop-level Carrollian scattering amplitudes in gauge theory and gravity, revealing their analytic structures, logarithmic behaviors, and IR divergence properties, using the modified Mellin prescription and extending known formulas.

Contribution

It introduces the computation of one-loop Carrollian amplitudes in gauge theory and gravity, generalizes results to all loops, and analyzes their IR divergence structure.

Findings

One-loop four-point Carrollian amplitudes in gauge theory retain tree-level analytic structure.

Explicit expressions for one-loop Carrollian MHV amplitudes in N=4 super Yang-Mills.

Carrollian amplitudes exhibit logarithmic behavior and factorization properties in IR regimes.

Abstract

Carrollian amplitudes are scattering amplitudes of massless particles written in position space at null infinity. We study various aspects of Carrollian amplitudes for gauge theory and gravity at loop level using primarily the modified Mellin prescription of [1]. Finite one-loop four-point Carrollian amplitudes in gauge theory are shown to maintain an analytic structure similar to tree level results. We compute the one-loop four-point Carrollian MHV amplitudes in planar $N=4$ super Yang-Mills theory, which are expressed as differential operators acting on tree level Carrollian amplitudes. This result is generalized to all loop orders using the Bern-Dixon-Smirnov (BDS) formula. Similar structures are observed at one-loop for Carrollian MHV amplitudes in $N=8$ supergravity. We next consider $2\to 2$ scattering of massless scalars via gravitational interactions in the eikonal regime and show that the corresponding Carrollian amplitudes exhibit logarithmic behavior in the `Carroll time' $u$. We compute the discontinuities of these Carrollian amplitudes up to $O(G^3)$ and show that they are descendants of Carrollian Born amplitudes. We observe similar logarithmic behavior in Carrollian amplitudes associated with the one-loop scalar box diagram. The dependence of this amplitude on dual scaling dimensions also differs from standard tree level results. Finally, we further study the infrared (IR) divergences of Carrollian amplitudes in massless scalar QED, gravity, and Yang-Mills theory. We show that Carrollian amplitudes in these theories naturally factorize, allowing us to provide an IR-safe definition for these objects.