Nonrelativistic spinning strings

TL;DR

This paper constructs nonrelativistic spinning string solutions in AdS_5 x S^5 within the SU(1,2|3) Spin-Matrix theory limit, deriving dispersion relations and connecting these solutions to integrable 1D models, revealing nontrivial spectrum corrections.

Contribution

It introduces explicit nonrelativistic spinning string solutions in the SMT limit and links them to integrable Neumann-Rosochatius models, providing new methods to estimate spectra in this regime.

Findings

Derived dispersion relations at strong coupling.

Constructed three-spin folded string configurations.

Showed spectrum corrections depend on string length in AdS_5.

Abstract

We construct nonrelativistic spinning string solutions corresponding to $ SU(1,2|3) $ Spin-Matrix theory (SMT) limit of strings in $ AdS_5 \times S^5 $. Considering various nonrelativistic spinning string configurations both in $ AdS_5 $ as well as $ S^5 $ we obtain corresponding dispersion relations in the strong coupling regime of SMT where the strong coupling ($ \sim \sqrt{\mathfrak{g}} $) corrections near the BPS bound have been estimated in the slow spinning limit of strings in $ AdS_5 $. We generalize our results explicitly by constructing three spin folded string configurations that has two of its spins along $ AdS_5 $ and one along $ S^5 $. Our analysis reveals that the correction to the spectrum depends non trivially on the length of the NR string in $ AdS_5 $. The rest of the paper essentially unfolds the underlying connection between $ SU(1,2|3) $ Spin-Matrix theory (SMT) limit of strings in $ AdS_5 \times S^5 $ and the nonrelativistic Neumann-Rosochatius like integrable models in 1D. Taking two specific examples of NR spinning strings in $ R \times S^3 $ as well as in certain sub-sector of $ AdS_5 $ we show that similar reduction is indeed possible where one can estimate the spectrum of the theory using 1D model.