Disconnected 2-group structures with charge conjugation

Develop a detailed analysis of the disconnected 2-group structure arising when the Z_2^C charge-conjugation symmetry is included in three-dimensional Ncale3 ChernSimons matter theories.

Background

The paper extends its 2-group framework to include the charge-conjugation symmetry Z2C\Z_2^C, which acts nontrivially on Wilson lines, the 1-form symmetry, and the 0-form symmetry group. In the $\Ncal=4$ examples, this produces semidirect-product structures and twisted Postnikov classes in an ω1\omega_1-twisted cohomology group.

The authors state that the corresponding disconnected 2-group structure has not yet been analysed in detail for the class of $\Ncal\geq3$ Chern\textendash Simons matter theories. This is therefore an explicitly identified unresolved extension of their symmetry analysis.

References

A more detailed analysis of the disconnected 2-group structure in the presence of the charge conjugation symmetry in the class of \Ncal \geq 3 CSM theories is open for future exploration.

— Generalised Symmetries, Anomalies, and Maximal Branches of 3d Chern-Simons Matter Theories  (2608.30349 - Marino et al., 31 Aug 2026) in Section "Remarks", subsection "Charge conjugation" (Section \ref{subsubsec:charge_conj})