Amplitudes of 3d Yang Mills Theory

TL;DR

This paper explores the properties of amplitudes in 3d super Yang Mills theory, including their derivation from 4d theories, dual conformal covariance at tree and loop levels, and explicit evaluation of one-loop amplitudes.

Contribution

It introduces a method to derive 3d amplitudes from 4d theories and demonstrates dual conformal covariance of tree and loop integrands in 3d super Yang Mills.

Findings

One-loop MHV amplitudes vanish.

One-loop non-MHV amplitudes are finite.

Tree amplitudes exhibit dual conformal covariance.

Abstract

This paper studies various properties of amplitudes in 3d super Yang Mills theory. First we explain how to obtain the amplitudes of 3d super Yang Mills theories from 4d super Yang Mills theories and obtain their helicity structure. Next, we use a 3d BFCW recursion relation to show that the tree amplitudes and loop integrands of maximal 3d super Yang Mills have dual conformal covariance (although not invariance, so that the amplitudes themselves are not dual conformal). Finally, we argue that the one-loop amplitudes of maximal 3d super Yang-Mills can be reduced to scalar box diagrams and evaluate these diagrams using dimensional regularization. We find that the one-loop MHV amplitudes vanish and the one-loop non-MHV amplitudes are finite.