On string S-matrix, bound states and TBA
By G. Arutyunov, S. Frolov. 2007
271 citations recorded by the source corpus.
The study of finite J effects for the light-cone AdS5???S5 superstring by means of the Thermodynamic Bethe Ansatz requires an understanding of a companion 2d theory which we call the mirror model. It is obtained from the original string model by the double Wick rotation. The S-matrices describing the scattering of physical excitations in the string and mirror models are related to each other by an analytic continuation. We show that the unitarity requirement for the mirror S-matrix fixes the S-matrices of both theories essentially uniquely. The resulting string S-matrix S(z1,?z2) satisfies the generalized unitarity condition and, up to a scalar factor, is a meromorphic function on the elliptic curve associated to each variable z. The double Wick rotation is then accomplished by shifting the variables z by quarter of the imaginary period of the torus. We discuss the apparent bound states of the string and mirror models, and show that depending on a choice of the physical region there are one, two or 2M?1 solutions of the M-particle bound state equations sharing the same conserved charges. For very large but finite values of J, most of these solutions, however, exhibit various signs of pathological behavior. In particular, they might receive a finite J correction to their energy which is complex, or the energy correction might exceed corrections arising due to finite J modifications of the Bethe equations thus making the asymptotic Bethe ansatz inapplicable.
Subfields: Geometry and Topology, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/95b8d7ca766ea232ddc893633e030edc20c8d816
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Citations in the corpus
- The quark anti-quark potential and the cusp anomalous dimension from a TBA equation (2012, background): “In the bulk of the worldsheet the mirror theory was discussed in various papers, see [29] for example.”
- Five loop Konishi from AdS/CFT (2009, background): “The corrections to the Asymptotic Bethe Ansatz can be identified with wrapping corrections [30], and the leading Lüscher corrections for single [31] and multiparticle states [32] have been derived for this (nonrelativistic) theory.”
- Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions (2014, unknown): “An example of a theory with a mirror rotation but no mirror symmetry is given by the theory of magnons over the BMN vacuum [56].”
- Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory (2015, background): “In this case there is no Z marker, in the conventions of [38, 39] that we shall follow.”
- Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model (2009, methodology): “To describe bound states of the mirror model, one should also add either the both lower or both upper edges of the cuts to the u-plane [34].”
- String hypothesis for the AdS5 × S5 mirror (2009, methodology): “1 Bethe-Yang equations The Bethe-Yang equations for fundamental particles and bound states of the mirror theory defined on a circle of large circumference R are derived by using the su(2|2)⊕ su(2|2)-invariant S-matrix [16] and the fusion procedure, and are of the form 1 = e pkR KI ∏”
- On the rotating and oscillating strings in (AdS3 × S3)ϰ (2014, background): “Infact more recently this problem of non-unitarity was resolved in [23] in a background known as mirror space [24] which is formally related to dS5 × H5 by a double T -duality.”
- Quantum deformations of the one-dimensional Hubbard model (2008, background): “Apart from the features discussed below, we expect it to have nice analytic properties analogous to the case of the undeformed case discussed in [38].”
- Four loop twist two, BFKL, wrapping and strings (2008, background): “Virtual particles and the exponential factor The virtual particles turn out to belong to the completely anti-symmetric representation of su(2|2)⊗su(2|2) first discussed in [58].”
- Extended Y-system for the AdS5/CFT4 correspondence (2010, unknown): “ effects in the Hubbard model [27]. The latter system is deeply related to the model studied in this paper. Starting from the mirror version of Beisert-Staudacher equations due to Arutyunov and Frolov [28] (see also [29]), the ground state TBA equations were recently and independently proposed in [30”
- Foundations of the AdS5 × S5 superstring: I (2009, methodology): “Later, it was found that the matrix structure of this S-matrix is uniquely fixed by the centrally-extended psu(2|2)⊕ psu(2|2) symmetry algebra, the Yang-Baxter equation and the generalized physical unitarity condition [16, 26, 27].”
- Four-loop perturbative Konishi from strings and finite size effects for multiparticle states (2008, background): “Yet when one considers the mirror theory (which exactly corresponds to the kinematic regime of the Lüscher F-term) it turns out [49] that it is the sl(2) poles which satisfy the physicality condition in the mirror theory.”
- Integrable Wilson loops (2012, unknown): “They are in the totally antisymmetric representations [51], which are homogenous polynomials in a pair of fermionic and a pair of bosonic variables with the opposite lables θ1, θ2, w3 and w4.”