The Bethe-Ansatz for N=4 Super Yang-Mills

Details The Bethe-Ansatz for N=4 Super Yang-Mills The Bethe-Ansatz for N=4 Super Yang-Mills

2002-12-17

arxiv.org/abs/hep-th/0212208v3

JHEP 0303 (2003) 013

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, 3 figures, LaTeX; v2 references added, typos corrected, \Lambda fixed; v3 expanded discussion of higher loops in con

Scientific paper

10.1088/1126-6708/2003/03/013

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.

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