The su(2|3) Dynamic Spin Chain

TL;DR

This paper provides evidence that the su(2|3) spin chain in N=4 superconformal gauge theory remains integrable at higher loop orders, despite the Hamiltonian not preserving the number of spin sites.

Contribution

It extends the integrability of the one-loop dilatation operator to three loops within the su(2|3) subsector, confirming a prior conjecture and analyzing the dynamic nature of the spin chain.

Findings

Energy shifts fixed up to three-loop level

Higher-loop Hamiltonian does not preserve spin sites

Supports integrability of the dynamic spin chain

Abstract

The complete one-loop, planar dilatation operator of the N=4 superconformal gauge theory was recently derived and shown to be integrable. Here, we present further compelling evidence for a generalisation of this integrable structure to higher orders of the coupling constant. For that we consider the su(2|3) subsector and investigate the restrictions imposed on the spin chain Hamiltonian by the symmetry algebra. This allows us to uniquely fix the energy shifts up to the three-loop level and thus prove the correctness of a conjecture in hep-th/0303060. A novel aspect of this spin chain model is that the higher-loop Hamiltonian, as for N=4 SYM in general, does not preserve the number of spin sites. Yet this dynamic spin chain appears to be integrable.