  In general warped compactifications, non-trivial backgrounds for the warp
factor and the dilaton break $D$-dimensional diffeomorphism invariance, so that
dilaton fluctuations can be gauged away completely and eaten by the metric.
More specifically, the warped volume modulus and the dilaton are not
independent, but combine into a single gauge-invariant degree of freedom in the
lower dimensional effective theory, the warped breathing mode. This occurs for
all strengths of the warping, even the weakly warped limit. This warped
breathing mode appears as a natural zero mode deformation of backgrounds
sourced by p-branes, and affects the identification of the independent degrees
of freedom of flux compactifications.
