Using topological operations to explore phase transitions beyond Landau

Simple operations such as gauging a discrete symmetry or stacking with an invertibe phase can be utilized to map familiar CFTs governing familiar phase transitions to less familiar scenario. I will discuss work that does this for both bosonic and fermionic theories in two spacetime dimensions. Starting from the Ising CFT, we obtain webs of CFTs that govern transitions involving nontrivial invertible phases of matter. Our work gives an explicit Lagrangian description of these CFTs and exhibits symmetry enriched quantum criticality in its natural habitat.