Abstract:
It is common belief that at zero temperature, a phase that spontaneously breaks a U(1)
symmetry becomes entirely superfluid, ie the normal density vanishes. This is indeed the case
in a variety of systems, such as weakly-coupled Helium, BCS superconductors and relativistic
superfluids described by a quantum effective action originally written by Son. Here, I will
show that this expectation fails in certain classes of holographic superfluids, such as those
with a Lifshitz-invariant critical ground state with Lifshitz exponent z¿d+2 (d is the number
of spatial dimensions), thus clarifying previous results in earlier literature. Time permitting,
I will conclude by commenting on the relevance of these results for recent measurements in
overdoped high Tc superconductors revealing an anomalously low superfluid density at odds
with BCS theory expectations.
