Semiclassical Strings on AdS_5 x S^5/Z_M and Operators in Orbifold Field Theories

TL;DR

This paper demonstrates agreement between semiclassical string energies and anomalous dimensions of operators in orbifold field theories derived from N=4 SYM, using Bethe ansatz solutions and twisted sectors in string theory.

Contribution

It provides the first detailed comparison of string energies and field theory anomalous dimensions in orbifold backgrounds, including twisted sectors and subsectors.

Findings

Agreement between string energies and anomalous dimensions in SU(2) subsectors

Bethe ansatz solvability of one-loop anomalous dimension matrices

Identification of twisted sectors in string configurations

Abstract

We show agreements, at one-loop level of field theory, between energies of semiclassical string states on AdS_5 x S^5/Z_M and anomalous dimensions of operators in N=0,1,2 orbifold field theories originating from N=4 SYM. On field theory side, one-loop anomalous dimension matrices can be regarded as Hamiltonians of spin chains with twisted boundary conditions. These are solvable by Bethe ansatz. On string side, twisted sectors emerge and we obtain some string configurations in twisted sectors. In SU(2) subsectors, we compare anomalous dimensions with string energies and see agreements. We also see agreements between sigma models of both sides in SU(2) and SU(3) subsectors.