The Bethe-ansatz for N = 4 super Yang-Mills

By J. Minahan, K. Zarembo. 2002

1,598 citations recorded by the source corpus.

We derive the one loop mixing matrix for anomalous dimensions in N=4 Super Yang-Mills. We show that this matrix can be identified with the Hamiltonian of an integrable SO(6) spin chain with vector sites. We then use the Bethe ansatz to find a recipe for computing anomalous dimensions for a wide range of operators. We give exact results for BMN operators with two impurities and results up to and including first order 1/J corrections for BMN operators with many impurities. We then use a result of Reshetikhin's to find the exact one-loop anomalous dimension for an SO(6) singlet in the limit of large bare dimension. We also show that this last anomalous dimension is proportional to the square root of the string level in the weak coupling limit.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/641a0eb2e0e70db5a4a2fb3984352b53839f3d0b

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In Nuclear and High Energy Physics

1. S. Frolov
2. A. Tseytlin
3. N. Beisert
4. G. Arutyunov
5. M. Staudacher
6. R. Roiban
7. K. Zarembo
8. Romuald A. Janik

Citations in the corpus

• Transcendentality and crossing (2006, neutral): “(2007) P 01021 Contents”
• Generalised integrable λ- and η-deformations and their relation (2015, background): “Most famously, the problem of determining the anomalous dimensions of single trace operators in the planar limit of N = 4 supersymmetric Yang–Mills gauge theory with gauge group SU(N) can be mapped to the problem of determining eigenvalues of an integrable spin-chain Hamiltonian [1].”
• Large spin limit of AdS5×S5 string theory and low energy expansion of ferromagnetic spin chains (2004, methodology): “The one [13], two [26] and three [26, 27, 28] loop dilatation operator of the N=4 SYM theory in the SU(2) (2 chiral scalar operator) sector has the form”
• Classical/quantum integrability in non-compact sector of AdS/CFT (2004, methodology): “The one-loop planar mixing matrix (dilatation operator) turns out to be a Hamiltonian of an integrable quantum spin chain [ 3 , 4]. The spin-chain Hamiltonian is a member of an infinite series of commuting charges and can be diagonalized by powerful techniques from the Bethe ansatz.”
• SPINNING STRINGS AND AdS/CFT DUALITY (2003, methodology): “Independently, it was observed in [22] that the oneloop planar anomalous dimension matrix in the pure-scalar sector of operators tr(ΦM1 ...ΦMJ ) can be interpreted as a Hamiltonian of an integrable SO(6) spin chain.”
• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory (2003, methodology): “Using the Bethe ansatz [25] is was possible to find states whose anomalous dimension can only be expressed in terms of elliptic functions [26].”
• Hidden Symmetries of the AdS_5 x S^5 Superstring (2003, background): “On the gauge side, Minahan and Zarembo [24] have shown that the calculation of oneloop anomalous dimensions for general scalar operators can be recast in terms of an integrable field theory (see further work [25]).”
• Dressing the Giant Magnon (2006, background): “Integrability on both sides of AdS/CFT [1,2,3,4,5] has enabled many quantitative checks of the correspondence (see [6,7,8,9,10] for reviews).”
• Integrability, spin-chains and the AdS3/CFT2 correspondence (2011, neutral): “Recall, that for a general (super)-Lie algebra with simple roots ~ αq we can write a set of Bethe equations in the representation give by weights ~ w as [61, 65]”