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The N=4 SYM Integrable Super Spin Chain

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arxiv hep-th/0307042 v3 pith:YCXDH4IA submitted 2003-07-03 hep-th cond-mathep-ph

Niklas Beisert , Matthias Staudacher This is my paper · ORCID
classification hep-thcond-mathep-ph
keywords integrablespinchainone-loopplanarsuperchainsdilatation
verification ladder T0 review T1 audit T2 compute T3 formal
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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 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 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.

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Cited by 4 Pith papers

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  1. Integrable systems: From the ice rule to supersymmetric fishnet Feynman diagrams

    hep-th 2025-09 conditional novelty 7.0 of 10

    A dissertation extends the integrability correspondence between lattice models and fishnet Feynman graphs to fermionic, supersymmetric, and boundary cases, yielding new exact critical couplings and a conjectured box p...

  2. Controlled Chaos in 4D SCFTs

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    Orbifolds of N=4 SYM produce SCFTs whose dilatation operator in a subsector is realized by a tunable spin chain whose eigenvalue statistics exhibit chaos for specific marginal couplings.

  3. Elliptical Wilson loops in ${\cal N}=4$ Super Yang-Mills

    hep-th 2025-09 conditional novelty 6.0 of 10

    A series expansion in eccentricity for elliptical Wilson loops in N=4 SYM, matching Dekel's strong-coupling area and giving a new one-loop weak-coupling correction.

  4. Probing weak chaos in $\mathcal N=4$ super Yang-Mills and long-range spin chains

    hep-th 2026-06 unverdicted novelty 5.0 of 10

    Finite-loop truncations of the planar dilatation operator in N=4 SYM exhibit GOE-like level statistics at large coupling for two- and four-loops (but not three), with eigenvector and Krylov diagnostics indicating weak...

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