Abstract
A flow invariant in quantum field theory is a quantity that doesnot depend on the flow connecting the UV and IR conformal fixedpoints. We study the flow invariance of the most general sumrule with correlators of the trace Θ of the stresstensor. In even (four and six) dimensions we recover the resultsknown from the gravitational embedding. We derive the sum rulesfor the trace anomalies a and a′ in six dimensions.In three dimensions, where the gravitational embedding is moredifficult to use, we find a non-trivial vanishing relation forthe flow integrals of the three- and four-point functions ofΘ. Within a class of sum rules containing finitely manyterms, we do not find a non-vanishing flow invariant of type ain odd dimensions. We comment on the implications of ourresults.
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