We consider a TFT on the product of a manifold with an interval, together with a topological and a non-topological boundary condition imposed at the two respective ends. The resulting (in general higher gauge) field theory is non-topological, with different choices of the topological conditions leading to field theories dual to each other. In particular, we recover the electric-magnetic duality, the Poisson-Lie T-duality, and we obtain new higher analogues thereof.
Different choices of the topological boundary condition in a TFT on M×I (with a fixed non-topological boundary at the other end) yield mutually dual non-topological (higher) gauge theories, and this mechanism reproduces electric-magnetic duality and Poisson-Lie T-duality as special cases while producing new higher-gauge dualities.
That a suitable bulk TFT with the required topological boundary conditions actually exists and is well-defined (non-perturbatively, or at least at the level needed) for each instance the authors invoke — particularly for the higher-gauge cases where the relevant higher categorical structures and their boundary theories are not standardly constructed.
1/ Take a topological field theory living on a manifold times an interval. Put a topological boundary condition on one end of the interval and a non-topological one on the other. Squash the interval: you get a non-topological theory on the manifold. 2/ Swap which topological boundary condition you used and you get a different non-topological theory — but it's dual to the first, because it came from the same bulk. This is the "sandwich" mechanism for duality. 3/ The authors claim this single picture recovers electric-magnetic duality and Poisson-Lie T-duality, and also produces new dualities for higher gauge theories (think gerbes and 2-form gauge fields), giving a non-abelian generalization.
Squish a stretchy theory between two walls. Pick different walls and you get different-looking theories that secretly mean the same thing.
Abstract-only review. The construction — sandwiching a TFT on M×I between a topological and a non-topological boundary condition to produce a non-topological boundary theory, with duality from swapping the topological boundary — is a recognized framework (cf. Kapustin–Saulina, Freed, Moore–Segal sandwich constructions). The claimed payoff (recovering EM duality, Poisson-Lie T-duality, and producing higher generalizations) is plausible and consistent with the authors' prior work on Poisson-Lie T-duality (Ševera et al.). I cannot verify without the body whether the "higher analogues" are genuinely new or repackagings, nor check the precise category-theoretic claims. No equations or theorems available to audit. Confidence is LOW; verdict UNVERDICTED on abstract alone, but the framing is mathematically reasonable and the authors have track record in this area.