Fermi Surfaces in General Codimension and a New Controlled Nontrivial Fixed Point

The energy of a d-dimensional Fermi system typically varies only along d[subscript c]=1 (“radial”) dimensions. We consider d[subscript c]=1+ε and study a transition to superconductivity in an ε expansion. The nontrivial fixed point describes a scale invariant theory with an effective space-time dimension D=d[subscript c]+1. Remarkably, the results can be reproduced by the Hertz-Millis action for the superconducting order parameter in higher effective space-time dimensions. We consider possible realizations of the transition at ε=1, which corresponds to a linear Fermi surface in d=3.National Science Foundatio