Conformal anomalies in 6d 4-derivative theories: a heat-kernel analysis

We compute the conformal anomalies for some higher-derivative (non-unitary) 6d Weyl invariant theories using the heat-kernel expansion in the background-field method. To this aim we obtain the general expression for the Seeley-DeWitt coefficient $b_6$ for four-derivative differential operators with background curved geometry and gauge fields, which was known only in flat space so far. We consider four-derivative scalars and abelian vectors as well as three-derivative fermions, confirming the result of the literature obtained via indirect methods. We generalise the vector case by including the curvature coupling $FF\mathrm{W}\mathrm{e}\mathrm{y}\mathrm{l}$.