We present two novel relations between the quasiparticle interaction in nuclear matter and the unique low momentum nucleon-nucleon interaction in vacuum. These relations provide two independent constraints on the Fermi liquid parameters of nuclear matter. Moreover, the new constraints define two combinations of Fermi liquid parameters, which are invariant under the renormalization group flow in the particle-hole channels. Using empirical values for the spin-independent Fermi liquid parameters, we are able to compute the major spin-dependent ones by imposing the new constraints as well as the Pauli principle sum rules.
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