Kinematic sum rules for trace anomalies

Abstract

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.

21 pages; published version: added discussion about scheme independence and generalization to sum rules for c

References in corpus (3)

• Anomalies, Unitarity and Quantum Irreversibility
• Exact Consequences of the Trace Anomaly in Four Dimensions
• A note on the improvement ambiguity of the stress tensor and the critical limits of correlation functions

Cited by in corpus (4)

• Inequalities for trace anomalies, length of the RG flow, distance between the fixed points and irreversibility
• Search for flow invariants in even and odd dimensions
• A note on the improvement ambiguity of the stress tensor and the critical limits of correlation functions
• On the $a$-theorem in the Conformal Window