Galois Orbits of TQFTs: Symmetries and Unitarity

Understand

We study Galois actions on $2+1$D 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).