  U(1) gauge theory of non-relativistic fermions interacting via compact U(1)
gauge fields in the presence of a Fermi surface appears as an effective field
theory in low dimensional quantum antiferromagnetism and heavy fermion liquids.
We investigate deconfinement of fermions near the Fermi surface in the
effective U(1) gauge theory. Our present analysis benchmarks the recent
investigation of quantum electrodynamics in two space and one time dimensions
($QED_3$) by Hermele et al. [Phys. Rev. B {\bf 70}, 214437 (2004)]. Utilizing a
renormalization group analysis, we show that the effective U(1) gauge theory
with a Fermi surface has a stable charged fixed point. Remarkably, the
renormalization group equation for an internal charge $e$ (the coupling
strength between non-relativistic fermions and U(1) gauge fields) reveals that
the conductivity $\sigma$ of fermions near the Fermi surface plays the same
role as the flavor number $N$ of massless Dirac fermions in $QED_3$. This leads
us to the conclusion that if the conductivity of fermions is sufficiently
large, instanton excitations of U(1) gauge fields can be suppressed owing to
critical fluctuations of the non-relativistic fermions at the charged fixed
point. As a result a critical field theory of non-relativistic fermions
interacting via noncompact U(1) gauge fields is obtained at the charged fixed
point.
