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The critical behavior of a non-local scalar field theory is studied. Thistheory has a non-local quartic interaction term which involves a real power-\beta of the Laplacian. The parameter \beta can be tuned so as to make thatinteraction marginal for any dimension. The lowest order Feynman diagramscorresponding to coupling constant renormalization, mass renormalization, andfield renormalization are computed. In all cases a non-trivial IR fixed pointis obtained. Remarkably, for dimensions different from 4, field renormalizationis required at the one-loop level. For d=4, the theory reduces to the usuallocal \phi^{4} field theory and field renormalization is required starting atthe the two-loop level. The critical exponents \nu and \eta are computed fordimensions 2,3,4 and 5. For dimensions greater than four, the critical exponent\eta turns out to be negative for \epsilon>0, which indicates a violation ofthe unitarity bounds.

Wilson-Fisher fixed points for any dimension