Six Directions in Anyon Condensation: Witt Classes, Fermionic Obstruction, and Condensation Lattices in Product Modular Tensor Categories

Key Points

• This research aims to explore the implications of anyon condensation in product modular tensor categories (MTCs) across multiple dimensions.
• Comprehensive analysis of 20 product modular tensor categories (MTCs)
• Investigated fermionic condensable algebras and their absence up to 10^10
• Explored properties of diamond condensation lattices and F-symbol dimensionality.
• Demonstrated universal Witt nontriviality across the studied categories
• Confirmed complete absence of fermionic condensable algebras
• Established that SU(4)_1^2 does not resolve to D(Z_4).