We consider string/M-theory reductions on a compact space X=Xloc∪X∘, where Xloc contains the singular locus and X∘ is its complement. For the resulting supergravity theories, we construct a suitable symmetry topological field theory (SymTFT) associated with the boundary ∂Xloc∐∂X∘. We propose that boundary conditions for different Bogomol’nyi-Prasad-Sommerfield branes wrapping the same boundary cycles must be correlated for the SymTFT to yield an absolute theory consistent with quantum gravity.
