6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications

TL;DR

This paper investigates the global symmetry structures of 6d SCFTs and their compactifications, revealing new classes of 4d $ abla$-N=2 SCFTs via Stiefel--Whitney twists and analyzing their symmetry properties.

Contribution

It provides a systematic method to determine the global form of symmetries in 6d SCFTs and constructs new 4d $ abla$-N=2 SCFTs through Stiefel--Whitney twisted compactifications.

Findings

Classifies global symmetry structures of 6d SCFTs.

Constructs new 4d $ abla$-N=2$ SCFTs via topologically non-trivial compactifications.

Links 6d theories to recently discovered 4d rank one and two SCFTs.

Abstract

The center-flavor symmetry of a gauge theory specifies the global form of consistent gauge and flavor bundle background field configurations. For 6d gauge theories which arise from a tensor branch deformation of a superconformal field theory (SCFT), we determine the global structure of such background field configurations, including possible continuous Abelian symmetry and R-symmetry bundles. Proceeding to the conformal fixed point, this provides a prescription for reading off the global form of the continuous factors of the zero-form symmetry, including possible non-trivial mixing between flavor and R-symmetry. As an application, we show that this global structure leads to a large class of 4d $\mathcal{N} = 2$ SCFTs obtained by compactifying on a $T^2$ in the presence of a topologically non-trivial flat flavor bundle characterized by a 't Hooft magnetic flux. The resulting "Stiefel--Whitney twisted" compactifications realize several new infinite families of 4d $\mathcal{N} = 2$ SCFTs, and also furnish a 6d origin for a number of recently discovered rank one and two 4d $\mathcal{N} = 2$ SCFTs.