End of the World Boundaries for Chiral Quantum Gravity Theories

We describe the construction of large classes of explicit string theory backgrounds corresponding to 6d and 4d chiral theories with end of the world boundaries, and describe the strong coupling phenomena involved in gapping the chiral (but non-anomalous) sets of fields, such as strongly coupled phase transitions or symmetric mass generation. One class of 6d constructions is closely related to chirality changing phase transitions, such as those turning heterotic NS5-branes into gauge instantons, in flat space or orbifold singularities. A class of 4d models exploits systems of IIB D3-branes at toric CY3 singularities with an extra $\mathbf{Z}_2$ involution related to $G_2$ holonomy manifolds in the type IIB picture and its IIA mirror, which we explicitly describe in terms of dimer diagrams.