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High Energy Physics - Theory, hep-th,
Abstract:
The one-dimensional Heisenberg XXX spin chain appears in a special limit of
the AdS/CFT integrable system. We review various ways of proving its
integrability, and discuss the associated methods of solution. In particular,
we outline the coordinate and the algebraic Bethe ansatz, giving reference to
literature suitable for learning these techniques. Finally we speculate which
of the methods might lift to the exact solution of the AdS/CFT system, and
sketch a promising method for constructing the Baxter Q-operator of the XXX
chain. It allows to find the spectrum of the model using certain algebraic
techniques, while entirely avoiding Bethe's ansatz.
