Abstract
We construct nonrelativistic spinning string solutions corresponding to SU(1, 2|3) Spin-Matrix theory (SMT) limit of strings in AdS5× S5. Considering various nonrelativistic spinning string configurations both in AdS5 as well as S5 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 AdS5. We generalize our results explicitly by constructing three spin folded string configurations that has two of its spins along AdS5 and one along S5. Our analysis reveals that the correction to the spectrum depends non trivially on the length of the NR string in AdS5. The rest of the paper essentially unfolds the underlying connection between SU(1, 2|3) Spin-Matrix theory (SMT) limit of strings in AdS5× S5 and the nonrelativistic Neumann-Rosochatius like integrable models in 1D. Taking two specific examples of NR spinning strings in R × S3 as well as in certain sub-sector of AdS5 we show that similar reduction is indeed possible where one can estimate the spectrum of the theory using 1D model.
Highlights
On the gauge theory side of the duality, the above limit (1.1) corresponds to operators with classical/tree level dimension ∆0 = J where all the other operators with ∆0 > J are essentially decoupled from the rest of the spectrum
Our analysis reveals that the correction becomes large as we move form single spin to multi-spin string configurations
The present paper explores various corners of the SU(1, 2|3) Spin-Matrix theory (SMT) limit of N = 4 SYM in the limit of strong coupling
Summary
One of the primary ambitions of the present paper is to construct various NR (semiclassical) spinning string configurations in AdS5 × S5 and explore the corresponding dispersion relations in the (large g 1) SU(1, 2|3) SMT limit of N = 4 SYM. √ (S g) limit of NR strings in AdS5 which has a dispersion relation of the form,. Considering spinning strings in S5, on the other hand, we notice that the dispersion relation takes the following form,. We discuss various decoupling limits associated to N = 4 SYM those may be interpreted as the degrees of freedom of a nonrelativistic string in the limit of strong coupling This provides a platform for several non trivial checks in nonrelativistic holographic correspondence using quantum mechanical degrees of freedom. The remaining angular variables {θ1, θ2, φ1, φ2} belong to the five sphere (S5) part of the original 10D target space geometry
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