Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations dualities, which is not immediately obvious. A prime example Scherk-Schwarz reductions double theory, have been shown to be one-to-one correspondence with Poisson-Lie T-duality. Here we demonstrate that this relation only the tip of iceberg. Currently, most general known...

The separability of the Hamilton-Jacobi equation has a well-known connection to existence Killing vectors and rank-two tensors. This paper combines this with detailed knowledge compactification metrics consistent truncations on spheres. fact that both inverse metric such compactifications, as well tensors can be written in terms bilinears underlying "round metric," enables us perform analyses f...