Giant Magnons

By D. Hofman, J. Maldacena. 2006

528 citations recorded by the source corpus.

Studies of N = 4 super Yang Mills operators with large R-charge have shown that, in the planar limit, the problem of computing their dimensions can be viewed as a certain spin chain. These spin chains have fundamental “magnon” excitations which obey a dispersion relation that is periodic in the momentum of the magnons. This result for the dispersion relation was also shown to hold at arbitrary ’t Hooft coupling. Here we identify these magnons on the string theory side and we show how to reconcile a periodic dispersion relation with the continuum worldsheet description. The crucial idea is that the momentum is interpreted in the string theory side as a certain geometrical angle. We use these results to compute the energy of a spinning string. We also show that the symmetries that determine the dispersion relation and that constrain the S-matrix are the same in the gauge theory and the string theory. We compute the overall S-matrix at large ’t Hooft coupling using the string description and we ﬁnd that it agrees with an earlier conjecture. We also ﬁnd an inﬁnite number of two magnon bound states at strong coupling, while at weak coupling this number is ﬁnite.

Subfields: Condensed Matter Physics, Electrical and Electronic Engineering, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b4858e176f6ef3f568496c4bd599019c0750d2ad

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Citations in the corpus

Magnon bound states and the AdS/CFT correspondence (2006, background): “(19) appears to be precisely the relevant BPS condition for all values of J2, generalising the single magnon result of [6].”
On the rotating and oscillating strings in (AdS3 × S3)ϰ (2014, background): “which is indeed the giant magnon dispersion relation in R× S2 as mentioned in [26].”
Dressing the Giant Magnon (2006, background): “In the example we look at below we will see that the class II soliton with four poles (3.17) in the complex plane can be obtained from an analytic continuation of two pairs of poles on the unit circle describing two class I solitons (3.16).”
On string theory on AdS3×S3×T4 with mixed 3-form flux: Tree-level S-matrix (2013, background): “In the semiclassical (“giant magnon” [44]) limit when h is large and p stays finite we get from (4.”
Foundations of the AdS5 × S5 superstring: I (2009, methodology): “Onesoliton solutions were identified with spin chain magnons and named “giant magnons” in [101].”
Notes on superconformal Chern-Simons-Matter theories (2007, background): “(For a sample of recent advances see [5,6,7,8,9,10,11,12,13].”
String hypothesis for the AdS5 × S5 mirror (2009, background): “To find the spectrum, one first takes the decompactification limit [8]-[11], i.”
The analytic Bethe ansatz for a chain with centrally extended symmetry (2006, background): “introduced in [35]. Here the parameters ϕk represent angles on a great circle of S5. In the ﬁgure, a string excitation with momentum pk corresponds to the line segments joining the points zk−1 and zk [34]. Conversely, the latter determine the position of the string between two excitations. Scatterin”
Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries (2010, methodology): “Giant magnons [19] on the LM background were constructed in [20] and [21], with the latter considering multispin configurations, while [22] considered more general rigid string solutions on the S(3)γ subspace, with the giant magnons and spiky strings as special cases.”
On three-point correlation functions in the gauge/gravity duality (2010, background): “Following the same steps, we move to the more complicated case of the giant magnon where the string rotates on a R×S2 subspace of AdS5×S [50].”
Transcendentality and crossing (2006, background): “ally unity to all orders in perturbation theory. This leads to various vexing discrepancies [15,16] with string theory results in the context of the AdS/CFT correspondence [17]. In fact, the S-matrix [4,18] of string theory on AdS 5 × S5 deﬁnitely requires a phase factor [19] as can be seen by compa”
Dressing and wrapping (2007, background): “z does not reproduce exponentially small terms in the size of the system [39]. A second indication comes from a study of the ﬁnite size eﬀects [40] on the 13 dispersion law of classical giant magnons [41]. Again, terms which fall oﬀ exponentially with the volume are seen which cannot easily be accou”
The quark anti-quark potential and the cusp anomalous dimension from a TBA equation (2012, methodology): “These soliton scattering phases were computed in [14,28].”