Field theory of higher-order topological crystalline response, generalized global symmetries and elasticity tetrads

I discuss aspects of higher-order topological field theory crystalline insulators with no other symmetries. show how the topology and geometry lattice is organized in terms so-called elasticity tetrads which are ground state degrees freedom labelling translational charges, higher-form conservation laws responses on sub-dimensional manifolds bulk insulator. The quasitopological obtained this way depend its embedding space, as expected for weak topology. In a insulator, they classify global symmetries transparent fashion generic dimensions. This hierarchy coincides dimensional terms, multipole expansion, anomaly inflow, related to mixed number electromagnetic gauge fields. continuum limit tetrads, semi-classical expansion momentum space can be used derive or subdimensional local U(1) symmetries, such fields, explicit formulas quasi-topological invariants Green’s functions. arbitrary dimensions readily generalized parameter allow e.g. pumping. simple results further bridge recently appreciated connections between theory, fields their relation fractonic excitations defects restricted mobility insulators.