Planar N=4 Gauge Theory and the Inozemtsev Long Range Spin Chain

By D. Serban, M. Staudacher. 2004

317 citations recorded by the source corpus.

We investigate whether the (planar, two complex scalar) dilatation operator of N = 4 gauge theory can be, perturbatively and, perhaps, non-perturbatively, described by an integrable long range spin chain with elliptic exchange interaction. Such a chain was introduced some time ago by Inozemtsev. In the limit of sufficiently “long” operators a Bethe ansatz exists, which we apply at the perturbative two- and three-loop level. Spectacular agreement is found with spinning string predictions of Frolov and Tseytlin for the two-loop energies of certain large charge operators. However, we then go on to show that the agreement between perturbative gauge theory and semi-classical string theory begins to break down, in a subtle fashion, at the three-loop level. This corroborates a recently found disagreement between three-loop gauge theory and near plane-wave string theory results, and quantitatively explains a previously obtained puzzling deviation between the string proposal and a numerical extrapolation of finite size three-loop anomalous dimensions. At four loops and beyond, we find that the Inozemtsev chain exhibits a generic breakdown of perturbative BMN scaling. However, our proposal is not necessarily limited to perturbation theory, and one would hope that the string theory results can be recovered from the Inozemtsev chain at strong ’t Hooft coupling.

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

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Citations in the corpus

Complete spectrum of long operators in N=4 SYM at one loop (2005, background): “which seems to be at the reach of our present possibilities is the generalization of the one-loop Bethe equations to two and three loops, as it was already done in a the smallest closed sectors su(2) [30] as well as u(1|1) and sl(2) [18], or even asymptotically in su(2) [15]. Our previous paper [47]”
Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT (2006, background): “5) (“3-loop disagreement” [34, 24]) while the first violation of the “semiclasical” scaling c30,1 6= 0 should thus appear at four loops.”
Quantum corrections to the string Bethe ansatz (2006, background): “However, in spite of this impressive results, disagreement is known to start at order λ3 [22, 23, 6].”
Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal (2008, background): “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.”
Long-range psu(2,2|4) Bethe Ansatze for gauge theory and strings (2005, background): “Therefore, the asymptotic generalization of the Bethe equations (2.22,2.26) for the su(1|1) sector of gauge theory apparently reads ( x+k x−k )L = K ∏ j=1 j 6=k 1− g2/2x+k x−j 1− g2/2x−k x+j .”
Algebraic Curve for the SO(6) Sector of AdS/CFT (2004, unknown): “ar X ∗Membre de l’Institut Universitaire de France”
Spinning strings in AdS5 × S5: one-loop correction to energy in SL(2) sector (2005, background): “ct comparison with perturbative anomalous dimensions of the corresponding single-trace operators in N = 4 SYM theory. Indeed, the precise agreement was established at the ﬁrst two leading orders in λ [5, 6, 7, 8, 9] (for reviews and further references see [10, 11, 12, 13, 14]). This agreement was fo”
The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability (2004, background): “5) is very likely to exist in contrast to the doubts raised in [87].”
Bethe ansatz for quantum strings (2004, methodology): “ions are derived assuming that both g and L are large, the comparison with gauge theory requires resummation of the gauge theoretic perturbative expansion, i.e. inclusion of the wrapping interactions [10, 11]. At present their structure is unknown. Moreover, the very notion of integrability becomes ”
A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills (2004, background): “njecture [8] based on the three-loop computation of[9]. The disagreement ﬁrst showed up inthenearBMN limit[27], andsubsequently inthe similarbut diﬀerent case of Frolov-Tseytlin (FT) spinning strings [13]. Assuming that the AdS/CFT correspondence is indeed correct and exact, a possible reason for th”
Planar N = 4 gauge theory and the Hubbard model (2005, background): “the Inozemtsev model [6] is ruled out [35] as an all-loop candidate.”
Wrapping interactions and a new source of corrections to the spin-chain/string duality (2005, background): “Whereas for the first of these three limits everything at the level of anomalous dimensions appears to work fine the latter two are plagued by vexing three-loop discrepancies [16, 17].”