Spin Matrix Theory String Backgrounds and Penrose Limits of AdS/CFT

TL;DR

This paper investigates the connection between Penrose limits of AdS${}_5 imes S^5$ and novel non-relativistic string backgrounds called flat-fluxed (FF) backgrounds within Spin Matrix theory limits, revealing their structure and relationships.

Contribution

It introduces and catalogs $U(1)$-Galilean backgrounds from SMT limits, shows their relation to Penrose limits, and demonstrates the commutation of these limits, advancing understanding of non-relativistic string geometries.

Findings

FF backgrounds are the simplest SMT string backgrounds.

Large charge limits of these geometries are analogous to Penrose limits.

SMT limits and Penrose limits commute, preserving background structures.

Abstract

Spin Matrix theory (SMT) limits provide a way to capture the dynamics of the AdS/CFT correspondence near BPS bounds. On the string theory side, these limits result in non-relativistic sigma models that can be interpreted as novel non-relativistic strings. This SMT string theory couples to non-relativistic $U(1)$-Galilean background geometries. In this paper, we explore the relation between pp-wave backgrounds obtained from Penrose limits of AdS${}_5 \times S^5$, and a new type of $U(1)$-Galilean backgrounds that we call flat-fluxed (FF) backgrounds. These FF backgrounds are the simplest possible SMT string backgrounds and correspond to free magnons from the spin chain perspective. We provide a catalogue of the $U(1)$-Galilean backgrounds one obtains from SMT limits of string theory on AdS${}_5 \times S^5$ and subsequently study large charge limits of these geometries from which the FF backgrounds emerge. We show that these limits are analogous to Penrose limits of AdS${}_5 \times S^5$ and demonstrate that the large charge/Penrose limits commute with the SMT limits. Finally, we point out that $U(1)$-Galilean backgrounds prescribe a symplectic manifold for the transverse SMT string embedding fields. This is illustrated with a Hamiltonian derivation for the SMT limit of a particle.