Let V be a vertex operator algebra, and for k a positive integer, let g be a k-cycle permutation of the vertex operator algebra V⊗k . We prove that the categories of weak, weak admissible and ordinary g-twisted modules for the tensor product vertex operator algebra V⊗k are isomorphic to the categories of weak, weak admissible and ordinary V -modules, respectively. The main result is an explicit...

This paper develops the foundations of a simplicial theory of weak ω-categories, which builds upon the insights originally expounded by Ross Street in his 1987 paper on oriented simplices. The resulting theory of weak complicial sets provides a common generalisation of the theories of (strict) ω-categories, Kan complexes and Joyal’s quasi-categories. We generalise a number of results due to the...

Abstract. We examine the periodic table of weak n-categories for the lowdimensional cases. It is widely understood that degenerate categories give rise to monoids, doubly degenerate bicategories to commutative monoids, and degenerate bicategories to monoidal categories; however, to understand this correspondence fully we examine the totalities of such structures together with maps between them ...

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_...