6d N=(2,0) theories are the source of many beautiful stories on supersymmetric field theories whose dimensions are lower than six. We hope similar and richer stories hold for 6d N=(1,0) theories, although it should be much harder to investigate with fewer supersymmetries.

As a first step, we want better understanding of 6d theories and some calculable quantities of those theories. We found that the anomaly polynomials of 6d N=(2,0) or N=(1,0) SCFTs can be determined on their tensor branch using a kind of anomaly maching mechanism similar to the Green-Schwarz mechanism. Each self-dual tensor fields associated to tensor branch scalars can have non-trivial Bianchi identities, which results in contribution to the anomaly additional to contribution from naive 1-loop calculation. Anomaly matching conditions uniquely determines such contributions, enabling us to calculate anomaly polynomials.

In this talk, I will review 6d N=(1,0) SCFTs which can be constructed with branes of the M-thoery, and then talk about anomaly polynomials. Especially, I will focus on the world volume theories of M5-branes on the ALE-singularities of general type.