6D RG Flows and Nilpotent Hierarchies

TL;DR

This paper classifies 6D superconformal field theory flows by analyzing nilpotent orbits and conformal matter vevs, revealing a hierarchy of IR fixed points and unbroken flavor symmetries.

Contribution

It introduces a systematic algebraic framework for understanding 6D SCFT RG flows via nilpotent hierarchies and conformal matter vevs, extending the classification of these theories.

Findings

Hierarchy of IR fixed points from nilpotent orbits

Tensor branch structures for each nilpotent orbit

Systematic computation of unbroken flavor symmetries

Abstract

With the eventual aim of classifying renormalization group flows between 6D superconformal field theories (SCFTs), we study flows generated by the vevs of "conformal matter," a generalization of conventional hypermultiplets which naturally appear in the F-theory classification of 6D SCFTs. We consider flows in which the parent UV theory is (on its partial tensor branch) a linear chain of gauge groups connected by conformal matter, with one flavor group G at each end of the chain, and in which the symmetry breaking of the conformal matter at each end is parameterized by the orbit of a nilpotent element, i.e. T-brane data, of one of these flavor symmetries. Such nilpotent orbits admit a partial ordering, which is reflected in a hierarchy of IR fixed points. For each such nilpotent orbit, we determine the corresponding tensor branch for the resulting SCFT. An important feature of this algebraic approach is that it also allows us to systematically compute the unbroken flavor symmetries inherited from the parent UV theory.