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(c)=1 ("radial") dimensions. We consider d(c)=1+epsilon and study a transition to superconductivity in an epsilon expansion. The nontrivial fixed point describes a scale invariant theory with an effective space-time dimension D=d(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 epsilon=1, which corresponds to a linear Fermi surface in d=3.