  Traditionally Fermi surfaces for problems in $d$ spatial dimensions have
dimensionality $d-1$, i.e., codimension $d_c=1$ along which energy varies.
Situations with $d_c >1$ arise when the gapless fermionic excitations live at
isolated nodal points or lines. For $d_c > 1$ weak short range interactions are
irrelevant at the non-interacting fixed point. Increasing interaction strength
can lead to phase transitions out of this Fermi liquid. We illustrate this by
studying the transition to superconductivity in a controlled $\epsilon$
expansion near $d_c = 1$. The resulting non-trivial fixed point is shown to
describe a scale invariant theory that lives in effective space-time dimension
$D=d_c + 1$. Remarkably, the results can be reproduced by the more familiar
Hertz-Millis action for the bosonic superconducting order parameter even though
it lives in different space-time dimensions.

Strongly Correlated Electrons;Superconductivity