2023/05/17 by Vladimir Bashmakov, Michele Del Zotto, Bashmakov, Vladimir +3
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.2305.10422
openalex publication_date 2023/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
In this paper we study the geometric origin of non-invertible symmetries of 2d theories arising from the reduction of 6d (2,0) theories on four-manifolds. This generalizes and extends our previous results in the context of class \mathcal S theories to a wider realm of models. In particular, we find that relative 2d field theories, such as the chiral boson, have a higher dimensional origin in four-manifolds that are not null cobordant. Moreover, we see that for the 2d theories with a 6d origin, the non-invertible symmetries have a geometric origin as a sum over topologies from the perspective of the 7d symmetry TFT. In particular, we show that the Tambara-Yamagami non-invertible symmetries TY(\mathbb ZN) can be given a geometric origin of this kind. We focus on examples that do not depend on spin structures, but we analyse the simplest of such cases, finding an interesting parallel between the extra choices arising in that context and symmetry fractionalization in Maxwell theories.