  Gauge symmetries are known to be respected by gravity because gauge charges
carry flux lines, but global charges do not carry flux lines and are not
conserved by gravitational interaction. For discrete symmetries, they are
spontaneously broken in the Universe, forming domain walls. Since the
realization of discrete symmetries in the Universe must involve the vacuum
expectation values of Higgs fields, a string-like configuration (hair) at the
intersection of domain walls in the Higgs vacua can be realized. Therefore, we
argue that discrete charges are also respected by gravity.
