  At large N_c, cold nuclear matter is expected to form a crystal and thus
spontaneously break translational symmetry. The description of chiral symmetry
breaking and translational symmetry breaking can become intertwined. Here, the
focus is on aspects of chiral symmetry breaking and its possible restoration
that are by construction independent of the nature of translational symmetry
breaking---namely spatial averages of chiral order parameters. A system will be
considered to be chirally restored provided all spatially-averaged chiral order
parameters are zero. A critical question is whether chiral restoration in this
sense is possible for phases in which chiral order parameters are locally
non-zero but whose spatial averages all vanish. We show that this is not
possible unless all chirally-invariant observables are spatially uniform. This
result is first derived for Skyrme-type models, which are based on a nonlinear
sigma model and by construction break chiral symmetry on a point-by-point
basis. A no-go theorem for chiral restoration (in the average sense) for all
models of this type is obtained by showing that in these models there exist
chirally symmetric order parameters which cannot be spatially uniform. Next we
show that the no-go theorem applies to large N_c QCD in any phase which has a
non-zero but spatially varying chiral condensate. The theorem is demonstrated
by showing that in a putative chirally-restored phase, the field configuration
can be reduced to that of a nonlinear sigma model.
