T-branes, anomalies and moduli spaces in 6D SCFTs

The worldvolume theory of M5-branes on an ADE singularity R-5/Gamma(G) can be Higgsed in various ways, corresponding to the possible nilpotent orbits of G. In the F-theory dual picture, this corresponds to activating T-brane data along two stacks of 7-branes and yields a tensor branch realization for a large class of 6D SCFTs. In this paper, we show that the moduli spaces and anomalies of these T-brane theories are related in a simple, universal way to data of the nilpotent orbits. This often works in surprising ways and gives a nontrivial confirmation of the conjectured properties of T-branes in F-theory. We use this result to formally engineer a class of theories where the IIA picture naively breaks down. We also give a proof of the alpha-theorem for all RG flows within this class of T-brane theories.