Form factors with two operator insertions and the principle of maximal transcendentality

TL;DR

This paper computes two-loop form factors with two operator insertions in maximally supersymmetric Yang-Mills theory, revealing new insights into transcendentality properties and the principle of maximal transcendentality.

Contribution

It provides the first calculation of two-point two-loop form factors with two identical operators in N=4 SYM, highlighting differences from single-operator cases and implications for transcendentality principles.

Findings

Two-loop form factors with two operators show lower transcendentality terms.

The highest transcendentality terms differ between double half-BPS and double Konishi FFs.

The principle of maximal transcendentality does not hold for two identical operator insertions.

Abstract

We present the first calculations of two-point two-loop form factors (FFs) with a two identical operators insertion in maximally supersymmetric Yang-Mills theory. In this article, we consider the supersymmetry protected half-BPS primary and unprotected Konishi operators. Unlike the FFs of a single operator insertion of the half-BPS primary, the FFs involving two half-BPS operators are found to contain lower transcendentality weight terms in addition to the highest ones. Moreover, in contrast to Sudakov FFs, the highest weight terms of the FFs of a double half-BPS no longer match with that of a double Konishi. We also find that the principle of maximal transcendentality, which dictates the presence of identical highest weight terms in the scalar FFs of half-BPS and quark/gluon FFs in QCD, does not hold true anymore for insertions of two identical operators. We discover the absence of any additional ultraviolet counterterm that could arise from the contact interaction between two composite operators.