Structure of Chern-Simons Scattering Amplitudes from Topological Equivalence Theorem and Double-Copy

Understand

We study the mechanism of topological mass-generation for 3d Chern-Simons (CS) gauge theories, where the CS term can retain the gauge symmetry and make gauge boson topologically massive.

• Without CS term the 3d massless gauge boson has a single physical transverse polarization state, while adding the CS term converts it into a massive physical polarization state and conserves the total physical degrees of freedom.
• We newly formulate the mechanism of topological mass-generation at $S$-matrix level.
• For this, we propose and prove a new Topological Equivalence Theorem (TET) which connects the $N$-point scattering amplitude of the gauge boson's physical polarization states ($A^a_{\rm{P}}$) to that of the transverse polarization states ($A^a_{\rm{T}}$) under high energy expansion.