  We derive from a microscopic model the effective theory of nematic order in a
system with a spontaneous quantum anomalous Hall effect in two dimensions.
Starting with a model of two-component fermions (a spinor field) with a
quadratic band crossing and short range four-fermion marginally relevant
interactions we use a 1/N expansion and bosonization methods to derive the
effective field theory for the hydrodynamic modes associated with the conserved
currents and with the local fluctuations of the nematic order parameter. We
focus on the vicinity of the quantum phase transition from the isotropic Mott
Chern insulating phase to a phase in which time-reversal symmetry breaking
coexists with nematic order, the nematic Chern insulator. The topological
sector of the effective field theory is a BF/Chern-Simons gauge theory. We show
that the nematic order parameter field couples with the Maxwell-type terms of
the gauge fields as the space components of a locally fluctuating metric
tensor. The nematic field has $z=2$ dynamic scaling exponent. The low energy
dynamics of the nematic order parameter is found to be governed by a Berry
phase term. By means of a detailed analysis of the coupling of the spinor field
of the fermions to the changes of their local frames originating from
long-wavelength lattice deformations we calculate the Hall viscosity of this
system and show that in this system is not the same as the Berry phase term in
the effective action of the nematic field, but both are related to the concept
of torque Hall viscosity which we introduce here.
