  We propose that local parity breaking induced by a large-scale fluctuation of
topological charge at large temperatures and/or condensation of pseudoscalar
mesons in the isotriplet channel for large baryon densities may be responsible
for the substantial dilepton excess that is found for low invariant masses and
moderate values of $p_T$ in central heavy ions collisions. This insofar
unexplained enhancement could be understood by a combination of two effects
leading both to an excess of $e^+e^-$ and $\mu^+ \mu^-$ pairs with respect to
theoretical predictions based on conventional hadronic processes: (a) a
modification of the dispersion relation of photons and vector mesons
propagating in such a nuclear medium due to local parity breaking; (b) the
appearance of new decay channels, forbidden by parity conservation in QCD in
the usual vacuum. Possible signatures of this effect and perspectives for its
detection are discussed.
