Wrapping interactions and a new source of corrections to the spin-chain/string duality

By J. Ambjørn, Romuald A. Janik, C. Kristjansen. 2005

332 citations recorded by the source corpus.

Abstract Assuming that the world-sheet sigma-model in the AdS/CFT correspondence is an integrable quantum field theory, we deduce that there might be new corrections to the spin-chain/string Bethe ansatz paradigm. These come from virtual particles propagating around the circumference of the cylinder and render Bethe ansatz quantization conditions only approximate. We determine the nature of these corrections both at weak and at strong coupling in the near-BMN limit, and find that the first corrections behave qualitatively as wrapping interactions at weak coupling.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6417638d85ebc0882aa42c9394a44f325fdee120

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Citations in the corpus

Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions (2014, methodology): “An example of a theory with a mirror rotation but no mirror symmetry is given by the theory of magnons over the BMN vacuum [73, 74].”
The analytic Bethe ansatz for a chain with centrally extended symmetry (2006, background): “A thermodynamic Bethe ansatz may be required to impose exact periodicity [61].”
Uniform Light-Cone Gauge for Strings in AdS5 x S5: Solving su(1|1) Sector (2005, background): “(1)Possible sources of the corrections to the gauge/string Bethe ansäte have been recently discussed in [25].”
The AdS 5 ×S 5 superstring worldsheet S matrix and crossing symmetry (2006, background): “One source of the discrepancy, the so called ‘wrapping interactions’ have apparently been ruled out [17, 18] so the problem remains open.”
Extended Y-system for the AdS5/CFT4 correspondence (2010, background): “This wrapping effect [11,18] is particularly relevant in the semiclassical string theory which covers the strong coupling regime though, for special reasons, it may not effect particular families of operators.”
Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model (2009, methodology): “l corrections to the particle energies computed via the Bethe-Yang equations. Derivation of the leading corrections by means of Lu¨scher’s approach [10] has been in the focus of recent investigations [11]-[20]. To obtain the ﬁnite L spectrum, one could try to generalize the Thermodynamic Bethe Ansat”
Five-loop anomalous dimension of twist-two operators (2009, background): “As for other integrable sigma models, the full solution to the spectral problem is believed to be given in terms of a set of TBA equations. There has been recently a lot of progress in this direction [25]-[29] and ultimately the Y-system [30] and the TBA equations for the ground state [31]-[33] have”
Transcendentality and crossing (2006, background): “Other promising approaches are the thermodynamical Bethe ansatz (see [51]) and Baxter equations (see [52]).”
Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory (2015, background): “One is the standard wrapping corrections which encircle each of the three operators [31].”
Dressing and wrapping (2007, result): “d from the way this Bethe ansatz was initially constructed [7]. The mechanism for the breakdown of the asymptotic approximation should be similar to the one discussed from a ﬁeld theory standpoint in [47], and from a lattice model point of view in [48]. Note added: Our results on twist-three operato”
Wrapping interactions at strong coupling: The giant magnon (2007, methodology): “ [27, 28] to derive the generalized formulas for the F- and µ-terms, recovering in the course of derivation the space-time interchange appearing as the motivation of the exponential terms proposed in [26]. Finally we used the formula for the generalized µ-term to evaluate ﬁnite size corrections to t”
Quantum corrections to the string Bethe ansatz (2006, methodology): “For an analysis of corrections to integrable quantum field theories on a cylinder in the AdS/CFT context see [38].”
Five loop Konishi from AdS/CFT (2009, background): “s [22]. 4 In order to ﬁnd the spectrum one has to pass to ﬁnite volume and consider the theory on a cylinder. The corrections to the Asymptotic Bethe Ansatz can be identiﬁed with wrapping corrections [29], and the leading Lu¨scher corrections for single [30] and multi-particle states [31] have been ”
Finite-size effects from giant magnons (2006, background): “bleading orders in 1/ √ λ. The strong coupling dispersion relation (2.17) is not modiﬁed in the Hubbard model, unlike what is observed here. Similarly, the quantum, ﬁnite size corrections computed in [3], seems to predict that the same exponential term governs ﬁnite size corrections at the quantum l”
Four loop twist two, BFKL, wrapping and strings (2008, background): “The leading contribution from wrapping will appear at order λ(4) which exactly matches the predictions coming from TBA type considerations [20].”