Nonrelativistic giant magnons and SU(1, 2|3) limit of strings in AdS5 × S

We derive nonrelativistic giant magnon spectrum starting from SU(1, 2|3) SpinMatrix theory (SMT) limit of strings in AdS5 × S5. The single spin as well as two spin nonrelativistic magnon spectrum are obtained considering rotating string configurations on R × Sp(p = 2, 3). In a parallel computation, we explore rigidly rotating string configurations in various sub-spaces of AdS5 and rediscover nonrelativistic magnon like excitations in these models. We further generalise our results by constructing a three spin solution where two of the spins are considered from S5 while the remaining one is aligned along S3 ⊂ AdS5. Unlike its relativistic cousins, our analysis reveals the non-existence of spikes in all of these nonrelativistic models. 1 Overview and Motivation The conjectured duality between the quantum mechanical/ Spin-Matrix theory (SMT) limit [1]-[5] of N = 4 SYM and the nonrelativistic strings [6]-[7] propagating in AdS5×S [8]-[9] has opened up a new era in the context of nonrelativstic gauge/string duality. Nonrelativistic string sigma models on curved manifolds seem to have two parallel formulations. One of these formulations is based on taking a large c limit of relativistic string theory on string Newton-Cartan (SNC) geometry [10]-[11]. In the second formulation, the nonrelativistic sigma model is obtained using the method of null reduction on a (relativistic) Lorentzian manifold [8]-[9]. As an end result of this null reduction procedure, one finally arrives at Polyakov/Nambu-Goto (NG) action for nonrelativistic strings propagating on a curved manifold that has a topology of torsional Newton-Cartan (TNC) geometry times a compact (periodic) direction along which the string has a non zero winding [12]-[21]. The resulting sigma model is nonrelativistic from the perspective of the target space geometry. However, interesting physics emerges after taking a second nonrelativistic (large c) limit on the worldsheet degrees of freedom. This is the limit which seems to provide a dual (stringy) description [8]-[9] for the near BPS sector in N = 4 SYM [5]. The purpose of this paper is to further zoom in into this sector for a better understanding of the holographic correspondence in a nonrelativistic set up. In particular, our goal would be to explore SU(1, 2|3) SMT limit of sigma models in AdS5 × S [8]-[9] and ∗E-mail: dibakarphys@gmail.com, dibakar.roychowdhury@ph.iitr. ac.in 1 ar X iv :2 01 0. 05 17 9v 1 [ he pth ] 1 1 O ct 2 02 0 establish its connection with various decoupling limits [1]-[5] in N = 4 SYM. Our analysis would eventually unfold nonrelativistic counterpart of some of the key observations carried out during the original formulation of the AdS5/CFT4 correspondence. One of the major successes of the celebrated AdS5/CFT4 correspondence is the precise matching of the operator spectrum using both gauge theory and the string theory degrees of freedom. On the gauge theory side of the duality, one typically looks for single trace operators ∼ tr(ΦX) (ΦX = φ1 + iφ2) with large R-charge (J 1) and large conformal dimension (∆ 1) such that the difference ∆−J = 0. In the presence of finite number of other fields (ΦZ = φ3 + iφ4), these operators/states may be interpreted as long spin chains with added impurities which are identified as elementary excitations associated with the spin chain known as magnons. Using SUSY, the dispersion relation (for any given values of the t’Hooft coupling (λ)) associated with these single spin magnons have been obtained in [22]. In the limit of strong coupling (λ 1), these magnon states precisely match with the Hofman-Maldacena limit [23] of semiclassical string states propagating in AdS5× S. A further probe into the dynamics of rotating strings in AdS5 × S reveals even a richer structure that goes under the name of spikes [24]-[25]. These are the rotating string solutions with n cusps where each cusp corresponds to the position of a scalar field (Φi) in the (higher twist) operator represented by tr(D 1Φ1 · · ·DΦn) with li 1. The single spin solutions of [22] were further generalised by taking into account the possibilities of forming magnon bound states in N = 4 SYM [26]. On the dual string theory side of the correspondence, these bound states would correspond to the rotating two spin folded string configurations on R×S [27]-[28]. The folded and circular two spin solutions in AdS5 × S were further generalised in [29] and a special infinite spin limit (in which the one loop correction to the classical string energy vanishes) was discussed. An intimate connection between these multispin string solutions [30] and the NeumannRosochatius (NR) integrable models was further investigated by authors in [31]. Keeping the spirit of the discussion as alluded to above, it is worthwhile to mention that a similar analysis in the context of the SMT limit of magnons in N = 4 SYM and in particular unfolding its connection with nonrelativistic rotating strings propagating in AdS5 × S is still lacking in the literature. The purpose of the present paper is therefore to fill up this gap by exploring the dynamics in the SU(1, 2|3) SMT limit of strings in AdS5 × S [9] and thereby providing a concrete map between the nonrelativistic stringy spectra and the corresponding SMT limit [5] of giant magnon dispersion relations in N = 4 SYM. In particular, our goal would be to construct a nonrelativistic analogue of multispin magnon bound states starting from single spin excitations. At the level of spin chains, we obtain magnon bound states by carefully considering the SMT limit [5] of the relativistic magnon dispersion relation in N = 4 SYM. We take the decoupling/quantum mechanical limit both in the weak as well as in the strong coupling regime of the SMT. A natural expectation would be to unveil a precise correspondence [5] between the nonrelativistic magnon spectra at strong coupling and the corresponding spectrum obtained in the SU(1, 2|3) SMT limit of strings in AdS5 × S [8]-[9]. To check this claim explicitly, we construct various rotating string configurations in different subsectors of AdS5 × S in the SU(1, 2|3) SMT limit [9] of the AdS5/CFT4 correspondence. Starting from a single spin solution on R × S we construct various multispin string solutions with spins aligned both along the directions of S as well as AdS5. As per our expectations, we find a precise agreement between the two sectors of the correspondence at strong coupling. The key ingradient behind the above matching