Evidence for C-theorems in 6D SCFTs

Using the recently established classification of 6D SCFTs we present evidence for the existence of families of weak C-functions, that is, quantities which decrease in a flow from the UV to the IR. Introducing a background R-symmetry field strength R, and a non-trivial tangent bundle T on the 6D spacetime, we consider C-functions given by the linear combinations C = m1α + m2β + m3γ, where the αi are the anomaly polynomial coefficients for the formal characteristic classes c2(R)2, c2(R)p1(T ) and p1(T )2. By performing a detailed sweep over many theories, we determine the shape of the unbounded region in “m-space” compatible with both Higgs branch flows and tensor branch flows. We also verify that — as expected — the Euler density conformal anomaly falls in the admissible region.