Computable conditions for order-2 CP symmetry in NHDM potentials

Abstract We derive necessary and sufficient conditions for order-2 CP (CP2) symmetry in N-Higgs-doublet potentials for N > 2. The conditions, which are formulated as relations between vectors that transform under the adjoint representation of SU(N) under a change of doublet basis, are representation theoretical in nature. Making use of Lie algebra and representation theory we devise an efficient, computable algorithm which may be applied to decide whether or not a given numerical potential is CP2 invariant.