On form factors in N=4 sym

TL;DR

This paper investigates form factors in N=4 SYM theory, revealing IR divergence exponentiation, anomalous dimensions, and complex finite parts involving polylogarithms, hinting at underlying integrable structures.

Contribution

It provides explicit calculations of form factors up to second order, highlighting their divergence structure and potential integrability signals in N=4 SYM.

Findings

IR divergences exponentiate with two anomalous dimensions

Finite parts involve generalized Goncharov polylogarithms

Results suggest underlying integrable structures

Abstract

In this paper we study the form factors for the half-BPS operators $\mathcal{O}^{(n)}_I$ and the $\mathcal{N}=4$ stress tensor supermultiplet current $W^{AB}$ up to the second order of perturbation theory and for the Konishi operator $\mathcal{K}$ at first order of perturbation theory in $\mathcal{N}=4$ SYM theory at weak coupling. For all the objects we observe the exponentiation of the IR divergences with two anomalous dimensions: the cusp anomalous dimension and the collinear anomalous dimension. For the IR finite parts we obtain a similar situation as for the gluon scattering amplitudes, namely, apart from the case of $W^{AB}$ and $\mathcal{K}$ the finite part has some remainder function which we calculate up to the second order. It involves the generalized Goncharov polylogarithms of several variables. All the answers are expressed through the integrals related to the dual conformal invariant ones which might be a signal of integrable structure standing behind the form factors.