The Matrix Product Ansatz for integrable U(1)^N models in Lunin-Maldacena backgrounds

Details The Matrix Product Ansatz for integrable U(1)^N models in Lunin-Maldacena backgrounds The Matrix Product Ansatz for integrable U(1)^N models in Lunin-Maldacena backgrounds

2008-02-26

arxiv.org/abs/0802.3802v1

Braz.J.Phys.38:237-244,2008

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1590/S0103-97332008000200005

We obtain through a Matrix Product Ansatz (MPA) the exact solution of the most general $N$-state spin chain with $U(1)^N$ symmetry and nearest neighbour interaction. In the case N=6 this model contain as a special case the integrable SO(6) spin chain related to the one loop mixing matrix for anomalous dimensions in ${\cal N} = 4$ SYM, dual to type $IIB$ string theory in the generalised Lunin-Maldacena backgrounds. This MPA is construct by a map between scalar fields and abstract operators that satisfy an appropriate associative algebra. We analyses the Yang-Baxter equation in the N=3 sector and the consistence of the algebraic relations among the matrices defining the MPA and find a new class of exactly integrable model unknown up to now.

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