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Archive for July 2001

I derive a procedure to generate sum rules for the trace anomalies $a$ and $a’$. Linear combinations of $\Delta a = a_{UV}-a_{IR}$ and $\Delta a’ = a’_{UV}-a’_{IR}$ are expressed as multiple flow integrals of the two-, three- and four-point functions of the trace of the stress tensor. Eliminating $\Delta a’$, universal flow invariants are obtained, in particular sum rules for $\Delta a$. The formulas hold in the most general renormalizable quantum field theory (unitary or not), interpolating between UV and IR conformal fixed points. I discuss the relevance of these sum rules for the issue of the irreversibility of the RG flow. The procedure can be generalized to derive sum rules for the trace anomaly $c$.

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JHEP 0111:033 (2001) | DOI: 10.1088/1126-6708/2001/11/033

arXiv:hep-th/0107194

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