  A flow invariant in quantum field theory is a quantity that does not depend
on the flow connecting the UV and IR conformal fixed points. We study the flow
invariance of the most general sum rule with correlators of the trace Theta of
the stress tensor. In even (four and six) dimensions we recover the results
known from the gravitational embedding. We derive the sum rules for the trace
anomalies a and a' in six dimensions. In three dimensions, where the
gravitational embedding is more difficult to use, we find a non-trivial
vanishing relation for the flow integrals of the three- and four-point
functions of Theta. Within a class of sum rules containing finitely many terms,
we do not find a non-vanishing flow invariant of type a in odd dimensions. We
comment on the implications of our results.
