We propose in this article that if the chemical potential exceeds a cr
itical value in dense hadronic medium, a first-order phase transition
to a new state of matter with Lorentz symmetry spontaneously broken (i
n addition to the explicit breaking) takes place. As a consequence, li
ght vector mesons get excited as ''almost'' Goldstone bosons. Since th
e light vector mesons dominantly couple to photons, the presence of th
ese new vector mesons could lead to an enhancement in the dilepton pro
duction from dense medium at an invariant mass lower than the free-spa
ce vector-meson mass. We provide a low-energy quark model which demons
trates that the above scenario is a generic case for quark theories wi
th a strong interaction in the vector channel. We discuss possible rel
evance of this phase to the phenomenon of the enhanced dilepton produc
tion at low invariant masses in relativistic heavy-ion collisions. (C)
1997 Elsevier Science B.V.