IAS CMP/QFT Group Meeting

Abstract: Fusion surface models, as introduced by Inamura and Ohmori, extend the concept of anyon chains to 2+1 dimensions, taking fusion 2-categories as their input. In this talk, I will focus on fusion surface models constructed from braided fusion 1-categories, which conserve (non-invertible) 1-form symmetries. I will discuss how Kitaev’s honeycomb model can be understood as an Ising fusion surface model and explore generalizations from the ZN Tambara-Yamagami and Fibonacci category, which are promising candidates for realizing chiral topological order. Finally, I will describe how bond-algebraic dualities between fusion surface models arise through different choices of module tensor categories over the underlying braided fusion category. This talk is based on arXiv:2408.04006 and upcoming work.