The SU(3) spin chain sigma model and string theory

By R. Hernández, Esperanza Lopez. 2004

148 citations recorded by the source corpus.

The ferromagnetic integrable SU(3) spin chain provides the one loop anomalous dimension of single trace operators involving the three complex scalars of N = 4 supersymmetric Yang-Mills. We construct the non-linear sigma model describing the continuum limit of the SU(3) spin chain. We find that this sigma model corresponds to a string moving with large angular momentum in the five-sphere in AdS5 × S 5 . The energy and spectrum of fluctuations for rotating circular strings with angular momenta along three orthogonal directions of the five-sphere is reproduced as a particular case from the spin chain sigma model.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/bbf8075d74b3ebb4906f3086f933baae68aa98f3

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In Nuclear and High Energy Physics

Citations in the corpus

Spinning strings in AdS5 × S5: one-loop correction to energy in SL(2) sector (2005, background): “The comparison of the reduced sigma model appearing in the “fast string” limit of the string action to the coherentstate (“Landau-Lifshitz”) action on the ferromagnetic spin chain side provided a simple and universal way of matching the string and gauge theory semiclassical states as well as near-by”
Towards integrability for AdS 3 / CFT 2 ?> (2014, background): “For several integrable strings backgrounds this is actually the case [61–66], and for instance in the case of AdS5/CFT4 the first evidence of integrability was discovered in four-dimensional N = 4 SYM theory precisely in form of the Heisenberg spin chain Hamiltonian by Minahan and Zarembo [67].”
Spiky strings and giant magnons on S5 (2006, unknown): “In that case one can also use coherent state methods to compare directly the actions for relevant low-energy modes on the string and the spin chain side [26, 30].”
Gauge-string duality for (non)supersymmetric deformations of N=4 super-Yang–Mills theory (2005, background): “In all previously discussed examples of similar comparisons the leading order terms in the two expressions matched, and our aim will be to extend this matching to the present (non-supersymmetric for unequal γi) case.”
Gauge-string duality for superconformal deformations of N=4 super Yang-Mills theory (2005, background): “In the limit of vanishing β-deformation one recovers the su(3) sector of N = 4 SYM which was analyzed in detail in [76, 77].”
Semiclassical relativistic strings in S 5 and long coherent operators in = 4 SYM theory (2004, methodology): “This connects and generalizes previous partial results of [16, 18, 20, 21].”
Algebraic Curve for the SO(6) Sector of AdS/CFT (2004, background): “Agreement for other particular examples [31– 34] as well as at the level of the Hamiltonian [35–42] was obtained until discrepancies surfaced at three-loops, first in the (near) BMN correspondence [43–46], later also for spinning strings [47].”
Strings with non-relativistic conformal symmetry and limits of the AdS/CFT correspondence (2018, methodology): “This procedure results in a sigma-model description in a semi-classical limit of the spin chain [14] (see also [15–19] and [4]).”