The Bethe Ansatz for Z_S Orbifolds of N=4 Super Yang-Mills Theory

TL;DR

The paper addresses whether integrability survives abelian $Z_S$ orbifolds of $N=4$ SYM and develops a Bethe Ansatz that accounts for the orbifold twist. It introduces a new quasi-excitation representing the orbifold generator and phase factors determined by the orbifold charges, producing one-loop Bethe equations that reproduce known anomalous dimensions and extend to BMN-like spectra. It analyzes several concrete orbifolds, including $N=1$ and $N=2$ cases, and explains how higher-loop Beisert equations and beta deformations can be incorporated. The work provides a practical framework for studying twisted sectors in AdS/CFT and points to connections with the sigma model, non-abelian orbifolds, and wrapping effects.

Abstract

Worldsheet techniques can be used to argue for the integrability of string theory on AdS_5xS^5/Z_S, which is dual to the strongly coupled Z_S-orbifold of N=4 SYM. We analyze the integrability of these field theories in the perturbative regime and construct the relevant Bethe equations.

Figures (1)

• Figure 1: Orbifold weights for the simple roots using the Dynkin diagrams "Beauty", "Beast" and "Higher" (from top to bottom). The leftmost root represents a site of the spin chain, a quasi-excitation of type $0$. The indicated numbers are the orbifold weights $s_j$ for each type of Bethe root.