Anomalies, renormalization group flows, and the α-theorem in six-dimensional (1,0) theories

We establish a linear relation between the alpha-type Weyl anomaly and the 't Hooft anomaly coefficients for the R-symmetry and gravitational anomalies in six-dimensional (1, 0) superconformal field theories. For RG flows onto the tensor branch, where conformal symmetry is spontaneously broken, supersymmetry relates the anomaly mismatch Delta a to the square of a four-derivative interaction for the dilaton. This establishes the alpha-theorem for all such flows. The four-derivative dilaton interaction is in turn related to the Green-Schwarz-like terms that are needed to match the 't Hooft anomalies on the tensor branch, thus fixing their relation to Delta a. We use our formula to obtain exact expressions for the a-anomaly of N small E-8 instantons, as well as N M5-branes probing an orbifold singularity, and verify the alpha-theorem for RG flows onto their Higgs branches. We also discuss aspects of supersymmetric RG flows that terminate in scale but not conformally invariant theories with massless gauge fields.