Topological Equivalence Theorem and Double-Copy for Chern-Simons Scattering Amplitudes

TL;DR

This paper introduces a Topological Equivalence Theorem linking gauge boson and transverse states in 3d Chern-Simons theories, reveals large energy cancellations in scattering amplitudes, and extends double-copy methods to massive graviton amplitudes.

Contribution

It proposes a new theorem connecting physical and transverse gauge boson amplitudes, uncovers large energy cancellations, and extends double-copy techniques to massive gravity in topological gauge theories.

Findings

Proved a general energy cancellation mechanism for gauge boson amplitudes.

Discovered large energy cancellations in four-graviton scattering amplitudes.

Established a correspondence between cancellations in gauge theory and gravity.

Abstract

We study the mechanism of topological mass-generation for 3d Chern-Simons gauge theories and propose a brand-new Topological Equivalence Theorem to connect scattering amplitudes of the physical gauge boson states to that of the transverse states under high energy expansion. We prove a general energy cancellation mechanism for $N$-point physical gauge boson amplitudes, which predicts large cancellations of $E^{4-L}\to E^{(4-L)- N}$ at any $L$-loop level ($L\geqslant 0$). We extend the double-copy approach to construct massive graviton amplitudes and study their structures. We newly uncover a series of strikingly large energy cancellations $E^{12}\to E^1$ of the tree-level four-graviton scattering amplitude under high energy expansion and establish a new correspondence between the two energy cancellations in the topologically massive Yang-Mills gauge theory and the topologically massive gravity theory. We further study the scattering amplitudes of Chern-Simons gauge bosons and gravitons in the nonrelativistic limit.