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Abstract We investigate the one-loop spectral problem of γ-twisted, planar N $$ \mathcal{N} $$ = 4 Super Yang-Mills theory in the double-scaling limit of infinite, imaginary twist angle and vanishing Yang-Mills coupling constant. This non-unitary model has recently been argued to be a simpler version of full-fledged planar N $$ \mathcal{N} $$ = 4 SYM, while preserving the latter model’s...