Classification of 6d N=(1,0) gauge theories

TL;DR

This work develops a systematic framework to classify 6d $\mathcal{N}=(1,0)$ gauge theories with semi-simple gauge groups by enforcing anomaly cancellation through the Green-Schwarz mechanism with tensor multiplets, global anomaly constraints, and quantization of instanton-string charges. It shows that theories fall into two UV-completion possibilities: when the Green-Schwarz matrix $c^{ab}$ is positive definite, the theory, if UV complete, must be a 6d SCFT; when $c^{ab}$ has a single zero eigenvalue, the theory corresponds to a little-string theory. The authors implement a quiver-based classification for theories with classical gauge groups, restrict representations to those with positive $c_R$ and bounded dimensions, and derive determinant criteria to distinguish admissible diagrams from forbidden ones. They provide explicit lists of potential SCFTs and little-string theories, including tri-fundamental and chain-like quivers, and they show that the instanton-string charge quantization condition follows from the anomaly data. The results illuminate the landscape of 6d $(1,0)$ theories, clarify the role of tensor moduli in UV behavior, and connect to known F-theory realizations and the broader framework of 6d dynamics.

Abstract

We delineate a procedure to classify 6d N=(1,0) gauge theories composed, in part, of a semi-simple gauge group and hypermultiplets. We classify these theories by requiring that they satisfy some consistency conditions. The primary consistency condition is that the gauge anomaly can be cancelled by adding tensor multiplets which couple to the gauge fields by acting as sources of instanton strings. Based on the number of tensor multiplets required to cancel the anomaly, we conjecture that the UV completion of these consistent gauge theories (if it exists) should be either a 6d N=(1,0) SCFT or a 6d N=(1,0) little string theory.