  We numerically compute the helicity modulus of the three-dimensional gauge
glass by Monte Carlo simulations. Because the average free energy is
independent of a twist angle, it is expected that the average helicity modulus,
directly related to the superfluid density, vanishes when simulations are
performed with periodic boundary conditions. This is not necessarily the case
for the typical (median) value, which is nonzero, because the distribution of
the helicity modulus among different disorder realizations is very asymmetric.
We show that the data for the helicity modulus distribution are well described
by a generalized extreme-value distribution with a nonzero location parameter
(most probable value). A finite-size scaling analysis of the location parameter
yields a critical temperature and critical exponents in agreement with previous
results. This suggests that the location parameter is a good observable. There
have been conflicting claims as to whether the superfluid density vanishes in
the vortex glass phase, with Fisher et al. [Phys. Rev. B 43, 130 (1991)]
arguing that it is finite and Korshunov [Phys. Rev. B 63, 174514 (2001)]
predicting that it is zero. Because the gauge glass is commonly used to
describe the vortex glass in high-temperature superconductors, we discuss this
issue in light of our results on the gauge glass.
