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

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 ($L⩾0$). 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.

arXiv comment8+5 pages, to match Journal Version. This Letter paper is a companion of the systematic longer paper arXiv:2110.05399 (46pp)

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Cited by in corpus (3)

• Massive Color-Kinematics Duality and Double-Copy for Kaluza-Klein Scattering Amplitudes
• Structure of Massive Gauge/Gravity Scattering Amplitudes, Equivalence Theorems, and Extended Double-Copy with Compactified Warped Space
• Equivalence Theorems and Double-Copy Structure in Scattering Amplitudes of Massive Kaluza-Klein States with Matter Interactions