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

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 nonrelativistic 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 ×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 × 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 × 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.

Classical string solutions in Non-Relativistic AdS$_5\times$S$^5$: Closed and Twisted sectors

“…This setting has been shown to be the natural framework to describe e.g. the Spin Matrix limit of AdS 5 ×S 5 [14,15,20]. Classical string solutions for this type of theory have been studied in e.g.…”

Null Dimensional Reduction of M2-Brane

“…In fact,there are basically two ways how to construct non-relativistic string theory. The first one is based on specific non-relativistic limit [37,28,34] while the second one on null reduction of the world-sheet string in arbitrary general background with null isometry [8,13,21,26]. It was then shown in [21] how these two non-relativistic string theories are related.…”

“…More precisely, we start with the relativistic string in the background with light-like isometry. Then performing T-duality along this direction we obtain string in torsional Newton-Cartan background [8,13,21,26], see also [17,20].…”

Canonical Analysis of Non-Relativistic String with Non-Relativistic World-Sheet

“…One can ask the question what is the dual description of this quantum mechanical model. It was suggested [3] and further studied in [6,5,7] that dual theory in the bulk corresponds to non-relativistic string theory with non-relativistic world-sheet known as SMT string. These special non-relativistic theories should be considered in the broader context of non-relativistic string theories that were studied recently in [3,5,6,7] and also [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22].…”

“…It was suggested [3] and further studied in [6,5,7] that dual theory in the bulk corresponds to non-relativistic string theory with non-relativistic world-sheet known as SMT string. These special non-relativistic theories should be considered in the broader context of non-relativistic string theories that were studied recently in [3,5,6,7] and also [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. This development is related to the generalization of Newton-Cartan geometry [23] to the stringy Newton-Cartan geometry [8] and torsional Newton-Cartan geometry.…”