Revision 2

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Title · changed: Revision 1: Does the a-anomaly decrease along all six-dimensional RG flows; Revision 2: Does the a-anomaly decrease along all six-dimensional RG flows?
Plain: In two and four dimensions a number counting effective degrees of freedom is proven to drop under coarse-graining. In six dimensions this is proven only for special supersymmetric cases.
Precise: In unitary 6D QFT, the Euler coefficient a of the trace anomaly is conjectured to satisfy $a_{UV} > a_{IR}$ for every RG flow between CFTs. The 4D dilaton proof (Komargodski and Schwimmer 2011) does not carry over because the relevant six-derivative dilaton coupling is not sign-definite by unitarity. Prove or refute the inequality for general, including non-supersymmetric, flows.
Settled by: A general argument (dilaton, entanglement or other) establishing $a_{\mathrm{UV}} > a_{\mathrm{IR}}$ in $d = 6$, or a unitary flow with $a_{\mathrm{UV}} \le a_{\mathrm{IR}}$.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: partially-resolved
Status note: Proven for supersymmetric tensor-branch flows and, in 2023-2025, orbi-instanton Higgs-branch flows; open in general.
Posed since: 1988

Decisions