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The Green's function of a weakly self-avoiding Levy walk with long range jumps in a large but finite cube in Z^3 can be expressed as the two point correlation function in a supersymmetric field theory. We have proved the global existence of the renormalization group trajectory of the underlying supersymmetric measure at all renormalization group scales . We establish the existence of the critical (stable) manifold and prove that the interactions are bounded away from zero on all scales. This is a step in a program to study rigorously the critical exponents of a self- avoiding Levy walk. Based on joint work with Benedetto Scoppola published in J.Stat Phys (2008) 133:921-1011.