  We give evidence that a population of pure contrarians globally coupled
D-dimensional Kuramoto oscillators reaches a collective synchronous state when
the interplay between the units goes beyond the limit of pairwise interactions.
Namely, we will show that the presence of higher order interactions may induce
the appearance of a coherent state even when the oscillators are coupled
negatively to the mean field. An exact solution for the description of the
microscopic dynamics for forward and backward transitions is provided, which
entails imperfect symmetry breaking of the population into a frequency-locked
state featuring two clusters of different instantaneous phases. Our results
contribute to a better understanding of the powerful potential of group
interactions entailing multi-dimensional choices and novel dynamical states in
many circumstances, such as in social systems.
