The dilatation operator of N=4 super Yang–Mills theory and integrability

Beisert, Niklas

doi:10.1016/j.physrep.2004.09.007

Cited by 562 publications

(1,451 citation statements)

References 194 publications

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“…It was then expected that we can interpolate these two regions by integrability and solve the theory completely. See reviews [3] for a summary of current progress and a list of references.…”

Section: Introductionmentioning

confidence: 99%

An exceptional algebraic origin of the AdS/CFT Yangian symmetry

Matsumoto¹,

Moriyama²

2008

J. High Energy Phys.

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In the su(2|2) spin chain motivated by the AdS/CFT correspondence, a novel symmetry extending the superalgebra su(2|2) into u(2|2) was found. We pursue the origin of this symmetry in the exceptional superalgebra d(2, 1; ε), which recovers su(2|2) when the parameter ε is taken to zero. Especially, we rederive the Yangian symmetries of the AdS/CFT spin chain using the exceptional superalgebra and find that the ε-correction corresponds to the novel symmetry. Also, we reproduce the non-canonical classical r-matrix of the AdS/CFT spin chain expressed with this symmetry from the canonical one of the exceptional algebra.

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Section: Introductionmentioning

confidence: 99%

An exceptional algebraic origin of the AdS/CFT Yangian symmetry

Matsumoto¹,

Moriyama²

2008

J. High Energy Phys.

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“…The energy of these semiclassical strings admits an expansion in the effective coupling λ/J 2 , with λ the 't Hooft coupling of the gauge theory, suggesting the possibility of a precise comparison between string energies and anomalous dimensions of large N = 4 Yang-Mills operators. However operator mixing turned the computation of anomalous dimensions for large N = 4 operators into a formidable task, until the illuminating identification of the planar dilatation operator [5,6] with the Hamiltonian of an integrable quantum spin chain [7,8]. The spectrum of anomalous dimensions for large operators became then computable using the powerful technique of the Bethe ansatz, and complete agreement with the energies of semiclassical string states was found at the first two leading orders in λ [9]- [25].…”

Section: Introductionmentioning

confidence: 99%

Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings

Hernández

López

Periáñez

et al. 2005

J. High Energy Phys.

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N = 4 supersymmetric Yang-Mills operators carrying large charges are dual to semiclassical strings in AdS 5 × S 5 . The spectrum of anomalous dimensions of very large operators has been calculated solving the Bethe ansatz equations in the thermodynamic limit, and matched to energies of string solitons. We have considered finite size corrections to the Bethe equations, that should correspond to quantum effects on the string side.

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“…More details regarding these root systems are given in Appendix A.2. The whole N = 4 theory was proved to be integrable [14], [15], [16]. Note that the spin chains with the different representations of su 2,2|4 correspond to different subclasses of operators.…”

Section: Bethe Equations: Chains With Arbitrary Symmetry Algebraementioning

confidence: 98%

“…One of them is the fact that the weak coupling on the gravity side (closed strings) corresponds to the strong coupling regime on the gauge theory side (open strings); and this prevents one from performing simple perturbative checks. It was major breakthrough when it was realized that some integrable structures were present in the scalar subsector of N = 4 SYM [13], and this result was extended to the complete set of operators in [14], [15], [16]. At the same time there was investigated the integrability of the closed string motion in [17] and the following works.…”

Section: Introductionmentioning

confidence: 99%