Anomaly matching on the Higgs branch

TL;DR

The paper develops a unified, geometry-driven approach to determine the full anomaly polynomial of certain supersymmetric theories by assuming their Higgs branch is the one-instanton moduli space $M_G$. By analyzing anomaly matching between the origin and a generic Higgs-point where the spectrum is free with unbroken symmetry $SU(2)_D\times G'$, the authors extract central charges and anomaly data across 6d, 4d, and 2d theories, including reproducing known results for the 6d E-string and 4d Minahan–Nemeschansky theories and predicting new constraints on non-Lagrangian theories. The method yields explicit consistency checks (and sometimes obstructions) via global anomalies, and it connects to ADHM constructions and bootstrap results, providing a powerful, cross-dimensional framework for understanding the landscape of high-dimensional SCFTs. Overall, the work offers a geometric, anomaly-based route to classify which groups $G$ can realize Higgs branches as $M_G$ and to compute their conformal data in the absence of conventional Lagrangian descriptions.

Abstract

We point out that we can almost always determine by the anomaly matching the full anomaly polynomial of a supersymmetric theory in 2d, 4d or 6d if we assume that its Higgs branch is the one-instanton moduli space of some group G. This method not only provides by far the simplest method to compute the central charges of known theories of this class, e.g. 4d E_{6,7,8} theories of Minahan and Nemeschansky or the 6d E-string theory, but also gives us new pieces of information about unknown theories of this class.