Galois orbits of TQFTs: symmetries and unitarity

Journal of High Energy Physics

Matthew Buican¹  Rajath Radhakrishnan¹ 

[1] CTP and Department of Physics and Astronomy, Queen Mary University of London, E1 4NS, London, UK;

关键词: Anyons;    Discrete Symmetries;    Topological Field Theories;    Chern-Simons Theories;   

DOI  :  10.1007/JHEP01(2022)004

来源: Springer

【 摘 要 】

We study Galois actions on 2+1D topological quantum field theories (TQFTs), characterizing their interplay with theory factorization, gauging, the structure of gapped boundaries and dualities, 0-form symmetries, 1-form symmetries, and 2-groups. In order to gain a better physical understanding of Galois actions, we prove sufficient conditions for the preservation of unitarity. We then map out the Galois orbits of various classes of unitary TQFTs. The simplest such orbits are trivial (e.g., as in various theories of physical interest like the Toric Code, Double Semion, and 3-Fermion Model), and we refer to such theories as unitary “Galois fixed point TQFTs”. Starting from these fixed point theories, we study conditions for preservation of Galois invariance under gauging 0-form and 1-form symmetries (as well as under more general anyon condensation). Assuming a conjecture in the literature, we prove that all unitary Galois fixed point TQFTs can be engineered by gauging 0-form symmetries of theories built from Deligne products of certain abelian TQFTs.

【 授权许可】

CC BY