It was recently shown that the string theory duals of certain deformations of the N=4 gauge theory can be obtained by a combination of T-duality transformations and coordinate shifts. Here we work out the corresponding procedure of twisting the dual integrable spin chain and its Bethe ansatz. We derive the Bethe equations for the complete twisted N=4 gauge theory at one and higher loops. These have a natural generalization which we identify as twists involving the Cartan generators of the conformal algebra. The underlying model appears to be a form of noncommutative deformation of N=4 SYM.
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