Penrose limit of MNa solution and spin chains in three-dimensional field theories

TL;DR

This paper explores the Penrose limit of the Maldacena-Nastase solution in three-dimensional theories, comparing string states in the resulting pp wave to spin chain models, revealing partial matches and suggesting explanations for discrepancies.

Contribution

It provides a detailed analysis of the Penrose limit of the MNa solution and its relation to spin chains in 3D field theories, highlighting partial correspondences and open questions.

Findings

Partial matching between pp wave string states and spin chain sectors.

Identification of features consistent with the Penrose limit analysis.

Discussion of possible reasons for the incomplete correspondence.

Abstract

In three dimensions, a theory with spontaneous breaking of supersymmetry was described holographically by the Maldacena-Nastase (MNa) solution. We revisit the issue of its Penrose limit, and compare the resulting pp wave and its string eigenstates to a sector of the theory on 5-branes reduced on $S^3$, and a spin chain-like system. We obtain many of the features of the pp wave analysis, but a complete matching still eludes us. We suggest possible explanations for the resulting partial mismatch, and compare against other spin chains for 3-dimensional field theories with gravity duals.