Bethe ansatz for quantum strings

By G. Arutyunov, S. Frolov, M. Staudacher. 2004

647 citations recorded by the source corpus.

We propose Bethe equations for the diagonalization of the Hamiltonian of quantum strings on AdS5 ×S 5 at large string tension and restricted to certain large charge states from a closed su(2) subsector. The ansatz differs from the recently proposed all-loop gauge theory asymptotic Bethe ansatz by additional factorized scattering terms for the local excitations. We also show that our ansatz quantitatively reproduces everything that is currently known about the string spectrum of these states. Firstly, by construction, we recover the integral Bethe equations describing semiclassical spinning strings. Secondly, we explain how to derive the 1/J energy corrections of M-impurity BMN states, provide explicit, general formulae for both distinct and confluent mode numbers, and compare to asymptotic gauge theory. In the special cases M = 2,3 we reproduce the results of direct quantization of Callan et al. Lastly, at large string tension and relatively small charge we recover the famous 2 4 √ n 2 � asymptotics of massive string modes at level n. Remarkably, this behavior is entirely determined by the novel scattering terms. This is qualitatively consistent with the conjecture that these terms occur due to wrapping effects in gauge theory. Our finding does not in itself cure the disagreements between gauge and string theory, but leads us to speculate about the structure of an interpolating Bethe ansatz for the AdS/CFT system at finite coupling and charge.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/002ccdb1febc343ac94b61f81aaa89883ffed494

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Citations in the corpus

Superstrings on AdS4 × ℂℙ3 as a coset sigma-model (2008, background): “Finite-gap solutions (including fermionic excitations) [18] could be also investigated with the goal of reconstructing the data of the string S-matrix undetermined by symmetries, e.g. the dressing phase [ 19 ].”
The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability (2004, background): “The same kind of disagreement was also observed for three excitations [129,102] and arbitrarily many of scalar type [130,131].”
Four loop twist two, BFKL, wrapping and strings (2008, background): “The Bethe Ansatz Equations have been derived [12, 13, 14, 15, 16, 17, 18, 19] giving the spectrum of states with large quantum numbers.”
Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal (2008, methodology): “This resolves the infamous “three-loop disagreement” [21] and implies [26] that the corresponding “string” Bethe Ansatz [30] should be modified to contain a non-trivial one-loop correction to the phase.”
Dressing the Giant Magnon (2006, methodology): “Using this map to sine-Gordon theory, the scattering phase of two magnons was computed and shown to match the large λ limit of the conjecture of [20].”
Magnon bound states and the AdS/CFT correspondence (2006, background): “A formula for SD was conjectured in [19] which passes many non-trivial tests but we will not need this here.”
Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model (2009, background): “There seems to be no proof of this assumption in [52], and in the appendix 2 of [51] a proof is given based on the AFS form [45] of the dressing phase.”
Integrability and the AdS3/CFT2 correspondence (2009, neutral): “At the lowest order in the strong-coupling expansion, h→ ∞, the dressing factor reduces to the AFS phase [20]:”
Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT (2006, methodology): “As in the previous work, we also find “nonanalytic” corrections related to non-trivial 1-loop phase in the corresponding Bethe ansatz S-matrix.”
Uniform Light-Cone Gauge for Strings in AdS5 x S5: Solving su(1|1) Sector (2005, background): “Recently, the knowledge of the classical string Bethe equations [11] together with the asymptotic gauge theory Bethe ansatz [16] allowed us to conjecture a novel Bethe ansatz [18] which is supposed to capture the leading quantum dynamics of strings in AdS5×S(5).”
The Algebraic Curve of Classical Superstrings on AdS5×S5 (2005, background): “Their conjecture of a quantitative agreement has been confirmed in several cases in [21, 22 ] and many more works since, 1 see [24‐28] for reviews of the subject.”
The Zamolodchikov-Faddeev Algebra for AdS5 x S5 Superstring (2006, background): “Here the gauge-independent dressing phase θ(p1, p2) [4] is a two-form on the vector space of conserved charges qn(p)”
Gauge-string duality for (non)supersymmetric deformations of N=4 super-Yang–Mills theory (2005, background): “est su(2)γ case in [2]). One may also hope that the analysis of the string Bethe equations will shed light on the structure of the dressing factor that appears in the Bethe ansatz for quantum strings [52] (in the deformed case the dressing factor may depend on γi and that may lead to an additional c”
A dynamic $ su{(1|1)^2} $ S-matrix for AdS3/CFT2 (2012, background): “To completely determine the S-matrix one needs to fix four antisymmetric phases that play a role similar to the dressing phase of AdS5 × S(5) strings [17, 18, 19].”
The all-loop integrable spin-chain for strings on AdS3 × S3 × T4: the massive sector (2013, background): “R.B., O.O.S. and A.S. acknowledge support by the Netherlands Organization for Scientific Research (NWO) under the VICI grant 680-47-602; their work is also part of the ERC Advanced grant research programme No. 246974, “Supersymmetry: a window to non-perturbative physics”.”
String hypothesis for the AdS5 × S5 mirror (2009, background): “where σ12 is the dressing factor [17] that depends on x ± and g.”
Dyonic giant magnons (2006, background): “sides of the correspondence strongly suggests that the problem is solvable and there has been signiﬁcant progress in formulating exact Bethe ansatz equations which hold for all values of the coupling [4, 5, 6, 7, 8]. In recent work, Hofman and Maldacena (HM) [9] have identiﬁed a particular limit whe”