  We study the low temperature tunneling density of states of thin wires where
superconductivity is destroyed through quantum phase-slip proliferation.
Although this regime is believed to behave as an insulator, we show that for a
large temperature range this phase is characterized by a conductivity falling
off at most linearly with temperature, and has a gapless excitation spectrum.
This novel conducting phase results from electron-electron interaction induced
pair breaking. Also, it may help clarify the low temperature metallic features
found in films and wires whose bulk realization is superconducting.
