  The reparametrization transformation between ultrametrically organised states
of replicated disordered systems is explicitly defined. The invariance of the
longitudinal free energy under this transformation, i.e. reparametrization
invariance, is shown to be a direct consequence of the higher level symmetry of
replica equivalence. The double limit of infinite step replica symmetry
breaking and n=0 is needed to derive this continuous gauge-like symmetry from
the discrete permutation invariance of the n replicas. Goldstone's theorem and
Ward identities can be deduced from the disappearence of the second (and higher
order) variation of the longitudinal free energy. We recall also how these and
other exact statements follow from permutation symmetry after introducing the
concept of "infinitesimal" permutations.
