The N=4 SYM Integrable Super Spin Chain

By N. Beisert, M. Staudacher. 2003

821 citations recorded by the source corpus.

Recently it was established that the one-loop planar dilatation generator of N = 4 Super Yang-Mills theory may be identified, in some restricted cases, with the Hamiltonians of various integrable quantum spin chains. In particular Minahan and Zarembo established that the restriction to scalar operators leads to an integrable vector so(6) chain, while recent work in QCD suggested that restricting to twist operators, containing mostly covariant derivatives, yields certain integrable Heisenberg XXX chains with non-compact spin symmetry sl(2). Here we unify and generalize these insights and argue that the complete one-loop planar dilatation generator of N = 4 is described by an integrable su(2,2|4) super spin chain. We also write down various forms of the associated Bethe ansatz equations, whose solutions are in one-to-one correspondence with the complete set of all one-loop planar anomalous dimensions in the N = 4 gauge theory. We finally speculate on the non-perturbative extension of these integrable structures, which appears to involve non-local deformations of the conserved charges.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/54a86b5fb8edc9d92b0ff07b1dc428cee66d52f2

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Citations in the corpus

SPINNING STRINGS AND AdS/CFT DUALITY (2003, methodology): “ction, evidence of integrable structures in the high-energy (near-conformal) limitofQCD appearedin[24,25,26,27,28], andsothespin chain relationofthethe 1- loop dilatation operator of N = 4 SYM theory [22, 23, 33] should have generalizations to other N = 1,2 supersymmetric theories (and not only in t”
Beauty and the twist: the Bethe ansatz for twisted = 4 SYM (2005, methodology): “However, in the study of the dilatation operator of gauge theories more general spin chains appear, most notably the spin chain based on the self-conjugate doubleton representation of psu(2,2|4), describing the dilatation operator of the full N = 4 SYM theory [22, 4 ].”
Pulsating strings on Ads(5) x S(5) (2004, background): “integrable Bethe spin chain [33], and are reviewed in [34]. The original results of [32] were restricted to the group SO(6) at 1-loop level, but were later extended 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”
The AdS 5 ×S 5 superstring worldsheet S matrix and crossing symmetry (2006, background): “Even more interestingly, the techniques of integrability allow in principle for an exact quantization of the superstring in AdS5 × S5 and/or the determination of anomalous dimensions in the N = 4 SYM.”
Bethe ansatz for quantum strings (2004, background): “In a parallel development, related recent advances in gauge theory came to be after the important observation that planar, conformal N = 4 SYM is an integrable system in the one-loop approximation [6, 7] and, very likely, at higher loops as well [8].”
An operator product expansion for polygonal null Wilson loops (2010, background): “However, we need to add the anomalous dimension per excitation δ∆ Lλ = 3 of the state tr ( F+i )L [24] to the result of [23].”
Complete spectrum of long operators in N=4 SYM at one loop (2005, methodology): “[ 12 ]. The dualization can be described in a compact schematic notation with the use of a sequence of Dynkin diagrams as illustrated in Fig. 2. Another”
The su(2|3) dynamic spin chain (2003, background): “[12] for a pedagogical introduction) to obtain the one-loop anomalous dimensions directly [5, 8].”
Matching Higher Conserved Charges for Strings and Spins (2003, background): “A similar but obviously more involved situation applies to arbitrary composite operators in N = 4 gauge theory, where the Bethe equations are also known [12].”
A relation between approaches to integrability in superconformal Yang-Mills theory (2003, methodology): “Thus, from our assumption about the free-field limit of the Yangian, we have been able, starting with the nonlocal symmetries found in [16], to deduce the basic conclusion of [11], found earlier in a special case in [9], that δD is a Hamiltonian of an integrable spin chain.”
String hypothesis for the AdS5 × S5 mirror (2009, background): “This would be done by employing the conjectured quantum integrability of the AdS5×S(5) superstring which is supported by classical integrability [2] of the Green-Schwarz action [3], and by one-loop integrability of the dual gauge theory [4, 5].”
Five-loop anomalous dimension of twist-two operators (2009, background): “on operator in certain subsectors of the gauge side of the correspondence was discovered. Later on [11], the complete one-loop datation operator and the one-loop Bethe e quations were written down in [12]. After many non-trivial steps [13] the form of the all-loop asymptotic Bethe equations (ABE) wa”
Gauge-string duality for superconformal deformations of N=4 super Yang-Mills theory (2005, background): “(2)This spin chain is explicitly known at the 1-loop level in the full theory [22], to the first few loop orders in various subsectors closed under renormalization group flow [23], and the asymptotic Bethe ansatz for the su(2) subsector were proposed in [24] (see [25] for a review and references).”