High-order topological phases host robust boundary states at the of boundary, which can be interpreted from their topology. In this work, considering interplay between superconductors and magnetic fields to gap surface three-dimensional weak insulators, we show that second-order (TSCs) featuring helical or chiral Majorana hinge modes third-order TSC corner realized. Remarkably, higher-order TSC...

We combine old and new quantum field theoretic arguments to show that any theory of stable or metastable higher spin particles can be coupled gravity only when the sector has a stringy structure. Metastable particles, free interacting, cannot couple while preserving causality unless there exist states in gravitational much below Planck scale $M_{\rm pl}$. obtain an upper bound on mass $\Lambda_...