Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops

TL;DR

This paper computes form factors of half-BPS operators in N=4 super Yang-Mills at tree and one loop, revealing a potential duality with periodic Wilson loops and expanding understanding of scattering amplitudes.

Contribution

It introduces a novel duality between form factors and periodic Wilson loops in N=4 SYM, using recursion and unitarity methods to compute one-loop form factors.

Findings

One-loop form factors with two scalars and positive-helicity gluons are explicitly calculated.

The form factors resemble MHV amplitudes, showing holomorphicity and expansion in two-mass easy box functions.

Agreement found between form factors and periodic Wilson loop calculations at one loop.

Abstract

We calculate form factors of half-BPS operators in N=4 super Yang-Mills theory at tree level and one loop using novel applications of recursion relations and unitarity. In particular, we determine the expression of the one-loop form factors with two scalars and an arbitrary number of positive-helicity gluons. These quantities resemble closely the MHV scattering amplitudes, including holomorphicity of the tree-level form factor, and the expansion in terms of two-mass easy box functions of the one-loop result. Next, we compare our result for these form factors to the calculation of a particular periodic Wilson loop at one loop, finding agreement. This suggests a novel duality relating form factors to periodic Wilson loops.