A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills

By N. Beisert, Virginia Dippel, M. Staudacher. 2004

547 citations recorded by the source corpus.

We probe the long-range spin chain approach to planar N = 4 gauge theory at high loop order. A recently employed hyperbolic spin chain invented by Inozemtsev is suitable for the su(2) subsector of the state space up to three loops, but ceases to exhibit the conjectured thermodynamic scaling properties at higher orders. We indicate how this may be bypassed while nevertheless preserving integrability, and suggest the corresponding all-loop asymptotic Bethe ansatz. We also propose the local part of the all-loop gauge transfer matrix, leading to conjectures for the asymptotically exact formulae for all local commuting charges. The ansatz is finally shown to be related to a standard inhomogeneous spin chain. A comparison of our ansatz to semi-classical string theory uncovers a detailed, non-perturbative agreement between the corresponding expressions for the infinite tower of local charge densities. However, the respective Bethe equations differ slightly, and we end by refining and elaborating a previously proposed possible explanation for this disagreement.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/16b160eb9717ee323c880a8b5fd5f32883701af3

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Citations in the corpus

Pulsating strings on Ads(5) x S(5) (2004, background): “tended to the full 1-loop SU(2,2|4) chain [35, 36], taking advantage of previous results on integrability in QCD amplitudes [37, 38]. Progress on higher orders in closed subsectors has also been made [39, 40, 41, 42]. The integrable spin chain formulation exposes the conserved charges. Conserved cha”
Dyonic giant magnons (2006, background): “The BPS condition essentially determines the dispersion relation for all these states to be [4, 6, 7, 8] (see also [11]),”
On three-point correlation functions in the gauge/gravity duality (2010, methodology): “Then, the contribution of the j-th magnon to the anomalous dimension of the operator OA is given by [4, 7, 44–46] γj(g) = √ 1 + 16g2 sin pj 2 − 1 .”
Gauge-string duality for superconformal deformations of N=4 super Yang-Mills theory (2005, methodology): “(28)To perform the comparison one should first rescale x and ξ: (x, ξ) → 4πL √ λ (x, ξ) , (29)The phase function was derived in [24] assuming the validity of the BMN scaling.”
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.”
Uniform Light-Cone Gauge for Strings in AdS5 x S5: Solving su(1|1) Sector (2005, background): “Finally, the (quantum) gauge and (classical) string theories reveal a certain interesting similarity between their integrable structures that can be manifested either through the study of infinite towers of conserved charges [13, 14, 15] or, equivalently, by comparing the corresponding Bethe equatio”
Five loop Konishi from AdS/CFT (2009, background): “the light-cone quantized Green-Schwartz superstring is currently almost completed. Historically, the developments which led to it concentrated on the Bethe Ansatz part mostly on the gauge theory side [11, 12, 13, 14, 15] as well as for classical string solutions in AdS5 × S5 [16, 17]. Later this was”
Foundations of the AdS5 × S5 superstring: I (2009, methodology): “The various pieces of the two-body scattering matrix were conjectured in [18, 19, 21] based on the analysis of the integral equations [22] describing classical spinning strings [23, 24, 25] and insights from gauge theory [17].”
Bethe ansatz for quantum strings (2004, background): “One intriguing result of [11], which will play a key role in this paper, was that the functional dependence of the individual charges of the elementary excitations (termed charge densities in [11]) on the excitation momenta agrees in the thermodynamic limit to all loop orders when one compares the (”
Wrapping interactions and a new source of corrections to the spin-chain/string duality (2005, methodology): “with λ being the ’t Hooft coupling constant and the qr’s certain conserved charges [18, 27].”
Finite-size effects from giant magnons (2006, background): “rgy of a string giant magnon is related to the momentum p ws by the formula E string = √ λ π ws sin p 2 , (2.17) which is the strong coupling, (i.e. λ → ∞) limit of the spin chain dispersion relation [27] E spin chain = r 1+ λ π2 sin2 p 2 , p ≡ p magnon. (2.18) This is an interesting result because ”
On string S-matrix, bound states and TBA (2007, background): “In what follows we need to know how the parameters x± introduced in [5] are expressed through p̃.”
Spinning strings in AdS5 × S5: one-loop correction to energy in SL(2) sector (2005, background): “er references see [10, 11, 12, 13, 14]). This agreement was found to break down (as in the near-BMN [3, 15] case [16]) at the next λ3 order [8, 9]. A natural explanation is an order-of-limits problem [8, 17, 18, 19]: on the string side one ﬁrst takes Jto be large to suppress quantum (α′) string corr”
The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations (2006, methodology): “ts which allow for an extrapolation to weak coupling λ ≪ 1 display a worrisome disagreement with the gauge theory results at the three loop order, which might be related to an order of limits problem [15]. Resolving this issue is a pressing problem for the AdS/CFT conjecture. The sigma-model describ”
String hypothesis for the AdS5 × S5 mirror (2009, background): “ssing factor [16]. Its general functional form was conjectured in [16] by discretizing the integral equations [17] describing classical spinning strings [18, 19], and using insights from gauge theory [20]. It was proposed in [21] that the dressing factor satisﬁes a crossing equation. Combining the f”
Quantum corrections to the string Bethe ansatz (2006, background): “In particular the tower of conserved charges is given by the same expressions in terms of the spectral parameter on both cases [7].”
Four-loop perturbative Konishi from strings and finite size effects for multiparticle states (2008, background): “From this they conjectured the finite size correction coming both from the modification of the Bethe Ansatz and from the effect of the sea of particles and anti-particles.”