One-Loop Holographic Weyl Anomaly in Six Dimensions

We compute $\mathcal{O}(1)$ corrections to the holographic Weyl anomaly for six-dimensional $\mathcal{N}=(1,0)$ and $(2,0)$ theories using the functional Schr"odinger method that is conjectured to work for supersymmetric theories on Ricci-flat backgrounds. We show that these corrections vanish for long representations of the $\mathcal{N}=(1,0)$ theory, and we obtain an expression for $\delta (c-a)$ for short representations with maximum spin two. We also confirm that the one-loop corrections to the $\mathcal{N}=(2,0)$ M5-brane theory are equal and opposite to the anomaly for the free tensor multiplet. Finally, we discuss the possibility of extending the results to encompass multiplets with spins greater than two.