Capacity bounds beyond untwisted WZW categories

Establish whether capacity bounds comparable to the quadratic topological-entanglement-entropy bound proved for untwisted Wess–Zumino–Witten modular tensor categories hold for coset constructions, twisted constructions, fermionic phases, and modular categories outside the WZW class.

Background

The paper proves that, within modular tensor categories arising from untwisted affine simple Lie algebras at positive integral levels, the maximal vacuum-flux torus topological entanglement entropy under a rank cutoff R grows asymptotically as 7ζ(3)/(4π²)². The balanced sequence Sp(2n)_n achieves the leading coefficient. The authors explicitly restrict this optimization to bosonic untwisted WZW theories and note that the result does not address broader classes of topological phases.

The unresolved question is whether an analogous capacity-versus-TEE bound, particularly the quadratic scaling or a suitably modified sharp asymptotic bound, persists when the admissible theories are enlarged to coset or twisted constructions, fermionic phases, or modular tensor categories not obtained from untwisted WZW models. Resolving this would determine the extent to which the WZW asymptotic benchmark reflects a general constraint rather than a feature of the selected theory class.