Study extends symmetries and anomalies of T[M] theories

What the study found: The article extends the study of symmetries and anomalies of T[M] theories to internal manifolds M that may have boundaries or defects. It reports that generalized symmetries, including higher-group and non-invertible symmetries, and their anomalies arise from combinations of the parent 6d symmetries and the geometry of M.
Why the authors say this matters: The authors suggest this helps organize how compactification shapes the symmetry structure of T[M] theories. They also present several topics they describe as of independent interest, including defect classification by framing response and connections involving u02c6Z_a and volume conjectures.
What the researchers tested: The study examines compactifications of 6d superconformal field theories, or SCFTs, on internal manifolds M. It uses examples with M of dimension 2, 3, and 4, and extends the idea of "polarizations on a manifold M" to cases with boundaries or defects.
What worked and what didn't: For 2-manifolds, the authors discuss the geometry of the "full moduli space" of T[M2] and its relation to polarizations and symmetries. For 3-manifolds, they describe the effect of torsion in homology on line operators in T[M3] and applications to quantum invariants such as u02c6Z_a(M3,q). For 4-manifolds, they give predictions for VOA[M4] and construct a new invariant depending on two q-parameters; the abstract does not describe any failed cases.
What to keep in mind: The abstract is a broad overview and does not give detailed proofs, numerical results, or a list of limitations. It also does not specify which examples establish each claim beyond indicating that examples in dimensions 2, 3, and 4 are used.

Key points

• The paper extends the study of symmetries and anomalies in T[M] theories to manifolds with boundaries or defects.
• It states that generalized symmetries, including higher-group and non-invertible ones, arise from 6d symmetries combined with the geometry of the internal manifold.
• For 3-manifolds, the authors discuss torsion in homology, line operators, and the invariant u02c6Z_a(M3,q).
• For 4-manifolds, the abstract mentions predictions for VOA[M4] and a new invariant depending on two q-parameters.