Anomalies, renormalization group flows, and the a -theorem in six-dimensional (1, 0) theories
Clay Córdova (Society of Fellows, Harvard University, Cambridge, MA, 02138, U.S.A.); Thomas Dumitrescu (Department of Physics, Harvard University, Cambridge, MA, 02138, U.S.A.); Kenneth Intriligator (Department of Physics, University of California, San Diego, La Jolla, CA, 92093, U.S.A.)
We establish a linear relation between the a -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 Δ a to the square of a four-derivative interaction for the dilaton. This establishes the a -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 Δ 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 a -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.
