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We demonstrate by explicit multi-loop calculation that \gamma-deformed planarN=4 SYM, supplemented with a set of double-trace counter-terms, has twonontrivial fixed points in the recently proposed double scaling limit,combining vanishing 't Hooft coupling and large imaginary deformationparameter. We provide evidence that, at the fixed points, the theory isdescribed by an integrable non-unitary four-dimensional CFT. We find a closedexpression for the four-point correlation function of the simplest protectedoperators and use it to compute the exact conformal data of operators witharbitrary Lorentz spin. We conjecture that both conformal symmetry andintegrability should survive in \gamma-deformed planar N=4 SYM for arbitraryvalues of the deformation parameters.

Strongly \gamma-deformed N=4 SYM as an integrable CFT