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We study an angular dipole deformation of maximally supersymmetric Yang-Mills theory (SYM) that preserves its classical scale invariance. We show that two-point functions of suitable single trace operators, restricted to an invariant plane, are determined by scaling dimensions computable from an integrable spin chain. This spin chain is a diagonally twisted version of the famous integrable spin chain of SYM. It matches expectations from the dual string theory perfectly, presenting a precision test of holography in this new setting, and an important step to understanding general twisted integrable AdS/CFT.

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