Twist-three at five loops, Bethe Ansatz and wrapping

TL;DR

This paper computes the five-loop anomalous dimension for twist-three operators in N=4 SYM, combining Bethe Ansatz and finite volume corrections, and confirms its consistency with theoretical expectations and resummation formulas.

Contribution

It provides the first complete five-loop anomalous dimension formula for twist-three operators, including asymptotic and wrapping effects, using Bethe Ansatz and Luescher formalism.

Findings

The result respects large spin scaling properties.

It passes non-trivial reciprocity tests.

Wrapping effects are of order log^2 M / M^2 for large M.

Abstract

We present a formula for the five-loop anomalous dimension of N=4 SYM twist-three operators in the sl(2) sector. We obtain its asymptotic part from the Bethe Ansatz and finite volume corrections from the generalized Luescher formalism, considering scattering processes of spin chain magnons with virtual particles that travel along the cylinder. The complete result respects the expected large spin scaling properties and passes non-trivial tests including reciprocity constraints. We analyze the pole structure and find agreement with a conjectured resummation formula. In analogy with the twist-two anomalous dimension at four-loops, wrapping effects are of order log^2 M/M^2 for large values of the spin.