Search for flow invariants in even and odd dimensions

Details Search for flow invariants in even and odd dimensions Search for flow invariants in even and odd dimensions

2002-09-28

arxiv.org/abs/hep-th/0209252v2

New J.Phys. 5 (2003) 11

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, v2: expanded introduction, published in NJP

Scientific paper

10.1088/1367-2630/5/1/311

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.

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