The anomalous current multiplet in 6D minimal supersymmetry

For supersymmetric gauge theories with eight supercharges in four, five and six dimensions, a conserved current belongs to the linear multiplet. In the case of six-dimensional $\mathcal{N}=(\mathcal{1},\mathcal{0})$ Poincar'e supersymmetry, we present a consistent deformation of the linear multiplet which describes chiral anomalies. This is achieved by developing a superform formulation for the deformed linear multiplet. In the abelian case, we compute a nonlocal effective action generating the gauge anomaly.