Soft theorems in Chern-Simons matter theories

We describe tree-level soft theorems for Chern-Simons QED and QCD in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>4</a:mn> <a:mo>+</a:mo> <a:mn>1</a:mn> </a:math> dimensions. Soft theorems have been studied in various context in the past. The universal behavior of the leading and subleading soft theorems is understood as a consequence of the local on-shell gauge invariance of the scattering amplitudes. Chern-Simons terms are gauge invariant only up to a boundary term. Hence, they make for an interesting case to study the relationship between gauge invariance and soft theorems. In this paper, we show that the subleading soft theorems in QED and QCD get corrected when Chern-Simons terms are introduced and also derive those corrections. We start with a discussion on soft theorems as a consequence of gauge invariance. Then we move on to derive the Chern-Simons vertices. Finally, we calculate the correction to soft theorems due to the addition of Chern-Simons terms for both QED and QCD.