Nonrelativistic spinning strings
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Springer
Received: August 21, Revised: September 23, Accepted: October 8, Published: November 10,
2020 2020 2020 2020
Dibakar Roychowdhury Department of Physics, Indian Institute of Technology Roorkee, Roorkee 247667, Uttarakhand, India
E-mail: [email protected] Abstract: We construct nonrelativistic spinning string solutions corresponding to SU(1, 2|3) Spin-Matrix theory (SMT) limit of strings in AdS5 × S 5 . Considering various nonrelativistic spinning string configurations both in AdS5 as well as S 5 we obtain corresponding dispersion relations in the strong coupling regime of SMT where the strong √ coupling (∼ 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 S 5 . 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 × S 5 and the nonrelativistic Neumann-Rosochatius like integrable models in 1D. Taking two specific examples of NR spinning strings in R × S 3 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. Keywords: AdS-CFT Correspondence, Long strings, Space-Time Symmetries ArXiv ePrint: 2008.08895
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP11(2020)044
JHEP11(2020)044
Nonrelativistic spinning strings
Contents 1 Overview and motivation 1.1 Spin-matrix theory and NR strings 1.2 Summary of results
1 1 2 4 5 5 6 8 8 9 10 10 11
3 Spinning strings in R × S 3 3.1 Constant radii solutions 3.2 Dispersion relation
12 13 14
4 Spinning strings in AdS5 4.1 Equations of motion 4.2 Energy-spin relation
14 15 15
5 Summary and final remarks
15
1 1.1
Overview and motivation Spin-matrix theory and NR strings
During last one decade, a series of work [1]–[7] have been put forward which essentially argues about a more tractable limit of the AdS5 /CFT4 correspondence [8]–[9] in a regime, ∆−J = fixed ; λ→0 λ
H = lim
N = fixed
(1.1)
where both the descriptions are under control and hence the corresponding spectrum could be subjected to a precise test. Here, ∆ is the energy of a state in N = 4 SYM on R×S 3 and J is a linear sum over Cartan charges. The above limit (1.1) essentially takes us towards a (nonrelativistic) corner of N = 4 SYM known as the Spin-Matrix theory (SMT) [6] where states in the Hilbert space carry indices both in the spin as well as adjoint representation.
–1–
JHEP11(2020)044
2 SU(1, 2|3) SMT limit and NR strings 2.1 Spinning strings in AdS5 2.1.1 Short strings 2.1.2 Extended strings 2.2 Spinning strings in S 5 2.2.1 Single spin solution 2.2.2 Multi-spin solutions 2.3 Folded three spin solutions 2.3.1 Perturbative solution 2.3.2 Energy
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