We introduce a Potts model with quenched, frustrated disorder, which enjoys
a gauge symmetry that forbids spontaneous magnetization and allows the gla
ssy phase to extend from T-c down to T = 0. We study numerically the four-d
imensional model with q = 4 states. We show the existence of a glassy phase
, and we characterize it by studying the probability distributions of an or
der parameter, the binder cumulant, and the divergence of the overlap susce
ptibility. We show that the dynamical behavior of the system is characteriz
ed by aging. [S0163-1829(99)10013-4].