Boundary topological orders of (4+1)d fermionic SPT states
This paper investigates (3+1)d topological orders with anomalous symmetry by microscopically constructing symmetry-preserving gapped boundary states for related (4+1)d SPT phases, demonstrating that such states admit a topological gauge theory description when , a non-TQFT solution when , and no symmetric gapped state otherwise, thereby confirming existing no-go theorems.