Collapsing-level conjecture for boundary VOAs of 3d mirror theories

Let a non-rank-zero 3d N=4\mathcal{N}=4 SQFT be a three-dimensional supersymmetric quantum field theory with nonzero rank, and let its boundary VOA be obtained after a topological twist. A collapsing level is a level at which the corresponding vertex operator algebra has the stated collapsing behavior. Collapsing-level conjecture. For non-rank-zero 3d N=4\mathcal{N}=4 SQFTs, their boundary VOAs after topological twists are at collapsing levels as a consequence of 3d mirror symmetry. The claim is presented as an expected consequence of 3d mirror symmetry; the supplied text does not state a proof or counterexample.

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Primary source

Shoma Sugimoto and Hao Li, “A Lie algebraic pattern behind logarithmic CFTs”, arXiv:2409.07381 (2026).

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