Two-Loop SL(2) Form Factors and Maximal Transcendentality

TL;DR

This paper computes two-loop form factors in the SL(2) sector of N=4 SYM, revealing patterns of maximal transcendentality and extending understanding of integrability and structure in gauge theories.

Contribution

It provides the first complete two-loop integrand and remainder functions for SL(2) form factors with arbitrary derivatives, highlighting maximal transcendentality patterns.

Findings

Full one-loop minimal form factor derived to all orders in dimensional regularisation.

Complete two-loop integrand constructed for operators with any number of derivatives.

Remainder functions exhibit patterns suggesting hidden maximal transcendentality.

Abstract

Form factors of composite operators in the SL(2) sector of N=4 SYM theory are studied up to two loops via the on-shell unitarity method. The non-compactness of this subsector implies the novel feature and technical challenge of an unlimited number of loop momenta in the integrand's numerator. At one loop, we derive the full minimal form factor to all orders in the dimensional regularisation parameter. At two loops, we construct the complete integrand for composite operators with an arbitrary number of covariant derivatives, and we obtain the remainder functions as well as the dilatation operator for composite operators with up to three covariant derivatives. The remainder functions reveal curious patterns suggesting a hidden maximal uniform transcendentality for the full form factor. Finally, we speculate about an extension of these patterns to QCD.