Dualities for Loop Amplitudes of N=6 Chern-Simons Matter Theory

TL;DR

This paper investigates loop corrections to four-point amplitudes in N=6 Chern-Simons matter theory, revealing a two-loop result matching N=4 super Yang-Mills and exploring dualities and computational simplifications.

Contribution

It introduces a duality between two-loop amplitudes in N=6 Chern-Simons theory and N=4 super Yang-Mills, and extends dimensional reduction methods to five dimensions.

Findings

One-loop amplitude vanishes as expected.

Two-loop amplitude is non-zero and matches Wilson loop results.

Dimensional reduction simplifies integral computations.

Abstract

In this paper we study the one- and two-loop corrections to the four-point amplitude of N=6 Chern-Simons matter theory. Using generalized unitarity methods we express the one- and two-loop amplitudes in terms of dual-conformal integrals. Explicit integration by using dimensional reduction gives vanishing one-loop result as expected, while the two-loop result is non-vanishing and matches with the Wilson loop computation. Furthermore, the two-loop correction takes the same form as the one-loop correction to the four-point amplitude of N=4 super Yang-Mills. We discuss possible higher loop extensions of this correspondence between the two theories. As a side result, we extend the method of dimensional reduction for three dimensions to five dimensions where dual conformal symmetry is most manifest, demonstrating significant simplification to the computation of integrals.