Challenge to the a theorem in six dimensions.

The possibility of a strong a theorem in six dimensions is examined in multiflavor ϕ^{3} theory. Contrary to the case in two and four dimensions, we find that, in perturbation theory, the relevant quantity a[over ˜] increases monotonically along flows away from the trivial fixed point. a[over ˜] is a natural extension of the coefficient a of the Euler term in the trace anomaly, and it arises in any even spacetime dimension from an analysis based on Weyl consistency conditions. We also obtain the anomalous dimensions and beta functions of multiflavor ϕ^{3} theory to two loops. Our results suggest that some new intuition about the a theorem is in order.