Distinquishing 4d N=2 SCFTs

TL;DR

This paper constructs examples of 4d N=2 SCFT pairs that are indistinguishable by certain invariants but differ in global flavor symmetry structure, revealing subtle distinctions in their global properties.

Contribution

It introduces a method to distinguish 4d N=2 SCFTs with identical invariants by analyzing their global flavor symmetry groups.

Findings

Pairs of SCFTs with identical invariants but different global flavor groups.

Differences detectable by superconformal index at high order.

Global flavor symmetry differences reflect subtle SCFT distinctions.

Abstract

We construct a family of examples of pairs of 4d N=2 SCFTs whose graded Coulomb branch dimensions, Weyl-anomaly coefficients and flavour symmetry algebras and levels coincide, but which are nonetheless distinct SCFTs. The difference (detectable by the superconformal index) can occur at arbitrarily high order. We argue that it is, however, reflected in a difference in the global form of the flavour symmetry groups.