Cutting through form factors and cross sections of non-protected operators in N=4 SYM

TL;DR

This paper computes the form factors of the Konishi operator in N=4 SYM using unitarity methods, addressing its dimension dependence, and derives related decay rates and anomalous dimensions up to two loops.

Contribution

It introduces a rigorous prescription for calculating Konishi form factors at all loops, including dimension dependence, and computes decay rates and anomalous dimensions up to two loops.

Findings

Derived a modification for unitarity calculations of the Konishi operator.

Computed two-loop two-point and one-loop three-point form factors.

Extracted the Konishi anomalous dimension up to two loops.

Abstract

We study the form factors of the Konishi operator, the prime example of non-protected operators in N=4 SYM theory, via the on-shell unitarity methods. Since the Konishi operator is not protected by supersymmetry, its form factors share many features with those in QCD, such as the occurrence of rational terms and of UV divergences that require renormalization. A subtle point is that this operator depends on the spacetime dimension. This requires a modification when calculating its form factors via unitarity methods. We derive a rigorous prescription that implements this modification to all loop orders and obtain the two-point form factor up to two-loop order and the three-point form factor to one-loop order. From these form factors, we construct an IR-finite cross section type quantity, namely the inclusive decay rate of the (off-shell) Konishi operator to any final (on-shell) state. Via the optical theorem, it is connected to the imaginary part of the two-point correlation function. We extract the Konishi anomalous dimension up to two-loop order from it.