Non-Fermi liquids in three dimensions

The shape of the fermi surface may have important effects in determining the relevance (in Renormalization group sense) of interactions for the underlying fermions. In our work, we show that for certain physically realizable fermi surfaces in three dimensions, the coupling of the fermions to critical bosons is relevant at the Gaussian fixed point. We find that such interactions may lead to a three dimensional non-Fermi liquid state. We calculate one-loop corrections to the electron self energy within a scheme of (3-$\epsilon$) perturbation in the spatial dimensions to understand the features of such a non-Fermi liquid state.