  We study the consequences of spatial coordinate transformation in multi-field
inflation. Among the spontaneously broken de Sitter isometries, only dilatation
in the comoving gauge preserves the form of the metric and thus results in
quantum-protected Slavnov-Taylor identities. We derive the corresponding
consistency relations between correlation functions of cosmological
perturbations in two different ways, by the connected and
one-particle-irreducible Green's functions. The lowest-order consistency
relations are explicitly given, and we find that even in multi-field inflation
the consistency relations in the soft limit are independent of the detail of
the matter sector.
