On-Shell Methods for the Two-Loop Dilatation Operator and Finite Remainders

TL;DR

This paper computes two-loop form factors in N=4 SYM to derive the dilatation operator and finite remainders, revealing universal leading transcendental parts and symmetry-based relations.

Contribution

It introduces on-shell unitarity methods to compute two-loop form factors and extract the dilatation operator in the SU(2) sector of N=4 SYM, including analysis of finite remainders.

Findings

Leading transcendentality part is universal and matches BPS expressions.

Finite remainders satisfy linear relations explained by R-symmetry Ward identities.

The two-loop dilatation operator is obtained from UV divergences of form factors.

Abstract

We compute the two-loop minimal form factors of all operators in the SU(2) sector of planar N=4 SYM theory via on-shell unitarity methods. From the UV divergence of this result, we obtain the two-loop dilatation operator in this sector. Furthermore, we calculate the corresponding finite remainder functions. Since the operators break the supersymmetry, the remainder functions do not have the property of uniform transcendentality. However, the leading transcendentality part turns out to be universal and is identical to the corresponding BPS expressions. The remainder functions are shown to satisfy linear relations which can be explained by Ward identities of form factors following from R-symmetry.