  We construct an effective field theory, a two-dimensional two-component
metallic system described by a model with two Fermi surfaces ("pockets"). This
model describes a translationally invariant metallic system with two types of
fermions, each with its own Fermi surface, with forward scattering
interactions. This model, in addition to the $O(2)$ rotational invariance, has
a $U(1) \times U(1)$ symmetry of separate charge conservation for each Fermi
surface. For sufficiently attractive interactions in the $d$-wave (quadrupolar)
channel this model has an interesting phase diagram that includes a
spontaneously generated anomalous Hall metal phase. We derive the
Landau-Ginzburg effective action of quadrupolar order parameter fields which
enjoys an $O(2)\times U(1)$ global symmetry associated to spatial isotropy and
the internal $U(1)$ relative phase symmetries respectively. We show that the
order parameter theory is dynamically local with a dynamical scaling of $z=2$
and perform a one-loop renormalization group analysis of the Landau-Ginzburg
theory. The electronic liquid crystal phases that result from spontaneous
symmetry breaking are studied and we show the presence of Landau damped
Nambu-Goldstone modes at low momenta that is a signature of non-Fermi liquid
behavior. Electromagnetic linear response is also analyzed in both the normal
and symmetry broken phases from the point of view of the order parameter
theory. The nature of the coupling of electromagnetism to the order parameter
fields in the normal phase is non-minimal and decidedly contains a precursor to
the anomalous Hall response in the form of a order-parameter-dependent
Chern-Simons term in the effective action.

Strongly Correlated Electrons