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

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Published 21 March 2003 • Published under licence by IOP Publishing Ltd
, , Citation Joseph A. Minahan and Konstantin Zarembo JHEP03(2003)013 DOI 10.1088/1126-6708/2003/03/013

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1 Department of Theoretical Physics, Box 803, SE-751 08 Uppsala, Sweden

Dates

  1. Received 30 January 2003
  2. Accepted 6 March 2003
  3. Published

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1126-6708/2003/03/013

Abstract

We derive the one loop mixing matrix for anomalous dimensions in Script 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/Jcorrections 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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10.1088/1126-6708/2003/03/013