Nonrelativistic spinning strings

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.