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

Jonathan J. Heckman, Craig Lawrie, Ling Lin, Hao Y. Zhang, Gianluca Zoccarato

TL;DR

The work develops a bottom-up framework to extract the full continuous global symmetry, including center and Abelian factors and possible R-symmetry mixing, of 6d SCFTs on their tensor branch via Green–Schwarz–Sagnotti–West topological couplings. This symmetry data then guides Stiefel–Whitney twisted compactifications on T^2, yielding a large landscape of 4d N=2 SCFTs, including numerous new infinite families and a 6d origin for many rank-1/2 theories. The authors provide a comprehensive set of examples, including orbi-instanton theories and their deformations, to demonstrate how the global form of symmetries constrains anomalies, central charges, and Coulomb-branch spectra across the SW-folds, with cross-checks against class S and S-fold constructions. The results illuminate deep connections between 6d tensor-branch data, background bundle topology, and the resulting 4d theories, and set the stage for exploring higher symmetries and broader dualities in this rich landscape.

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.

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

TL;DR

The work develops a bottom-up framework to extract the full continuous global symmetry, including center and Abelian factors and possible R-symmetry mixing, of 6d SCFTs on their tensor branch via Green–Schwarz–Sagnotti–West topological couplings. This symmetry data then guides Stiefel–Whitney twisted compactifications on T^2, yielding a large landscape of 4d N=2 SCFTs, including numerous new infinite families and a 6d origin for many rank-1/2 theories. The authors provide a comprehensive set of examples, including orbi-instanton theories and their deformations, to demonstrate how the global form of symmetries constrains anomalies, central charges, and Coulomb-branch spectra across the SW-folds, with cross-checks against class S and S-fold constructions. The results illuminate deep connections between 6d tensor-branch data, background bundle topology, and the resulting 4d theories, and set the stage for exploring higher symmetries and broader dualities in this rich landscape.

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 SCFTs obtained by compactifying on a 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 SCFTs, and also furnish a 6d origin for a number of recently discovered rank one and two 4d SCFTs.
Paper Structure (42 sections, 263 equations, 2 figures, 8 tables)

This paper contains 42 sections, 263 equations, 2 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Tensor Branch of 6d SCFTs
  3. Topology of Global Symmetry Group for 6d SCFTs
  4. Anomalies for Center--Flavor Symmetry
  5. Examples
  6. Example 1:
  7. Example 2:
  8. Example 3:
  9. Anomalies for Center Symmetries of Abelian Factors
  10. Abelian Charge Normalization
  11. Hypermultiplets
  12. E-String Contributions
  13. Examples
  14. Example 1:
  15. Example 2:
  16. ...and 27 more sections

Figures (2)

  • Figure 1: The subsector of the nilpotent hierarchy of the 6d SCFT in equation \ref{['eq:6d_trivialOrbit']} in which each theory enjoys a $\mathbb{Z}_3$ center-flavor symmetry. We listed the quiver description of the tensor branch and the partition defining the nilpotent orbit in each case. The $\mathbb{Z}_3$ Stiefel--Whitney twisted torus compactification of the theories appearing here gives rise to the 4d $\mathcal{N}=2$ SCFTs whose nilpotent network is depicted in Figure \ref{['fig:sfold_nilpotent_4d']}.
  • Figure 2: The nilpotent hierarchy of 4d $\mathcal{N}=2$ SCFTs obtained from nilpotent deformations breaking the $\mathfrak{su}_6$ flavor symmetry of $\mathcal{T}_3^{(N)}(1,1,3)$. The structure of the network matches that of the 6d SCFTs in Figure \ref{['fig:sfold_nilpotent']}, and the $\mathbb{Z}_3$ Stiefel--Whitney twisted compactifications of each of those 6d SCFTs yields the associated 4d SCFT in this figure.