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Theoretical and Mathematical Physics

The form factor program: A review and new results, the nested SU(N) off-shell Bethe ansatz and the 1/N expansion

H. Babujian, Angela Foerster, M. Karowski

Published Apr 1, 2008• 9 citations
Publisher
DOI
10.1007/s11232-008-0042-7

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The system of SU(N)- and U(N)-matrix difference equations are solved by means of a nested version of a generalized Bethe ansatz, also the called `off shell' Bethe ansatz (Babujian H M 1990 Correlation functions in WZNW model as a Bethe wavefunction for the Gaudin magnets Proc. XXIVth Int. Symp. (Ahrenshoop, Zeuthen)). To solve this new Bethe ansatz in the algebraic language analogous to the conventional case, a new type of monodromy matrices is introduced. They fulfil a new type of Yang - Baxter equations which simplify the proofs. Using a similar approach as for the conventional nested Bethe ansatz the problem is solved iteratively. The vanishing of the `unwanted terms' of the first level ansatz is equivalent to a set of second level difference equations. The solutions are obtained as sums over `off-shell' Bethe vectors. These sums are `Jackson-type integrals'. The highest weight property of the solutions is proved. The solutions are calculated explicitly for several examples of SU(N)- and U(N)-representations.