N=2 Super Yang-Mills and the XXZ spin chain

TL;DR

This paper studies the renormalization of scalar operators in N=2 Super Yang-Mills theory, revealing an integrable XXZ spin chain structure and discussing implications for dual supergravity backgrounds.

Contribution

It establishes a connection between the anomalous dimensions of operators in N=2 SYM and the Hamiltonian of an integrable XXZ spin chain, highlighting a novel integrability aspect.

Findings

Anomalous dimension matrix matches XXZ spin chain Hamiltonian

The anisotropy parameter Delta>1 relates to supergravity fluxes

Gauge coupling running does not affect one-loop RG equations

Abstract

We analyse the renormalisation properties of composite operators of scalar fields in the N=2 Super Yang-Mills theory. We compute the matrix of anomalous dimensions in the planar limit at one-loop order in the 't Hooft coupling, and show that it corresponds to the Hamiltonian of an integrable XXZ spin chain with an anisotropy parameter Delta>1. We suggest that this parameter could be related to the presence of non-trivial two-form fluxes in the dual supergravity background. We find that the running of the gauge coupling does not affect the renormalization group equations for these composite operators at one-loop order, and argue that this is a general property of gauge theories which is not related to supersymmetry.