Swampland Constraints on the SymTFT of Supergravity

Understand

We consider string/M-theory reductions on a compact space $X=X^\text{loc} \cup X^\circ$, where $X^\text{loc}$ contains the singular locus, and $X^\circ$ its complement.

• For the resulting supergravity theories, we construct a suitable Symmetry Topological Field Theory (SymTFT) associated with the boundary $\partial X^\text{loc} \coprod \partial X^\circ$.
• We propose that boundary conditions for different BPS branes wrapping the same boundary cycles must be correlated for the SymTFT to yield an absolute theory consistent with quantum gravity.
• Using heterotic/M-theory duality, this constraint can be translated into a field theoretic statement, which restricts the global structure of $d\geq 7$, $\mathcal{N}=1$ supergravity theories to reproduce precisely the landscape of untwisted toroidal heterotic compactifications.