Swampland Constraints on the SymTFT of Supergravity

TL;DR

This paper explores how swampland constraints influence the Symmetry Topological Field Theory (SymTFT) in supergravity, linking boundary conditions of branes to quantum gravity consistency and restricting supergravity theories to known string theory landscapes.

Contribution

It introduces a novel swampland constraint on SymTFT boundary conditions, connecting geometric singularities with global symmetry structures in supergravity theories.

Findings

Boundary conditions of BPS branes must be correlated for consistency.

Constraints reproduce the landscape of heterotic compactifications.

Gauged symmetries explain boundary conditions in 6d theories.

Abstract

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. Furthermore, for 6d $(2,0)$ theories, we utilize a subtle interplay between gauged 0-, 2-, and 4-form symmetries to provide a bottom-up explanation of the correlated boundary conditions in K3 compactifications of type IIB.