Axial anomalies of maximally supersymmetric tensor theories

We revisit anomalies of (4, 0) and (3, 1) maximally supersymmetric tensor theories in d = 6. A (4, 0) on-shell tensor multiplet descends to that of the d = 5 maximal supergravity upon a dimensional reduction, hypothesized to offer a strong-coupled UV completion of the latter in the same sense of (2, 0) theories as the UV completion of d = 5 $\mathcal{N}$ \( \mathcal{N} \) = 2 pure Yang-Mills. The gravitational anomalies, found to be nonvanishing, had been computed, although its relevance in the absence of the d = 6 metric is not obvious. We perform a comprehensive anomaly computation for (4, 0) and (3, 1) tensor supermultiplets, respectively, for Sp(4) and Sp(3) × Sp(1) R-symmetry anomalies and the mixed R-gravitational anomaly thereof, and find that anomalies involving R-symmetries cancel out identically. We close with questions on how to address the anomaly in this class of theories with no general covariance.