  We consider the phase diagram of hadronic matter as a function of
temperature, T , and baryon chemical potential, mu. Currently the dominant
paradigm is a line of first order transitions which ends at a critical
endpoint.
  In this work we suggest that spatially inhomogenous phases are a generic
feature of the hadronic phase diagram at nonzero mu and low T . Familiar
examples are pion and kaon condensates. At higher densities, we argue that
these condensates connect onto chiral spirals in a quarkyonic regime. Both of
these phases exhibit the spontaneous breaking of a global U(1) symmetry and
quasi-long range order, analogous to smectic liquid crystals. We argue that
there is a continuous line of first order transitions which separate spatially
inhomogenous from homogenous phases, where the latter can be either a hadronic
phase or a quark-gluon plasma.
  While mean field theory predicts that there is a Lifshitz point along this
line of first order transitions, in three spatial dimensions strong infrared
fluctuations wash out any Lifshitz point. Using known results from inhomogenous
polymers, we suggest that instead there is a Lifshitz regime. Non-perturbative
effects are large in this regime, where the momentum dependent terms for the
propagators of pions and associated modes are dominated not by terms quadratic
in momenta, but quartic. Fluctuations in a Lifshitz regime may be directly
relevant to the collisions of heavy ions at (relatively) low energies,
sqrt(s)/A : 1 to 20 GeV.
