An all order identity between ABJM and N=4 SYM four-point amplitudes

TL;DR

This paper establishes an exact algebraic relation between ABJM and N=4 SYM four-point amplitudes across all orders, revealing deep connections and enabling predictions for higher-loop amplitudes.

Contribution

It derives an all-order identity linking ABJM and N=4 SYM amplitudes, extending previous partial results and proposing an iterative formula for three-dimensional amplitudes.

Findings

Exact algebraic identity between two-loop ABJM and one-loop N=4 SYM amplitudes

Conjecture of an all-orders relation based on the BDS ansatz

Derivation of an almost complete four-loop ABJM amplitude

Abstract

We derive an exact algebraic identity between the two-loop four-point amplitude in ABJM theory and the corresponding one-loop amplitude in N=4 SYM theory. This identity generalizes previous partial results to an exact relation valid at all orders in the IR regulator. Moreover, it allows to conjecture an exact iterative expression for the complete three dimensional amplitude in terms of the BDS ansatz for the four dimensional one, indicating that the strict relation between the two amplitudes experimented at two loops might propagate to all orders. In particular, an almost complete expression for the ABJM amplitude at four loops is derived.