T-branes, Anomalies and Moduli Spaces in 6D SCFTs

TL;DR

This paper explores the relationship between T-branes, anomalies, and moduli spaces in 6D SCFTs, revealing universal connections to nilpotent orbit data and confirming properties of T-branes in F-theory.

Contribution

It establishes a universal relation between moduli spaces, anomalies, and nilpotent orbits in T-brane theories, and proves the $a$-theorem for these theories.

Findings

Moduli spaces and anomalies relate simply to nilpotent orbit data.

The results confirm conjectured properties of T-branes in F-theory.

Proof of the $a$-theorem for RG flows in T-brane theories.

Abstract

The worldvolume theory of M5-branes on an ADE singularity $\mathbb{R}^5/\Gamma_G$ 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 na\"ively breaks down. We also give a proof of the $a$-theorem for all RG flows within this class of T-brane theories.