One-Loop Holographic Weyl Anomaly in Six Dimensions

Understand

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.