Duality cascades and parallelotopes

Abstract Duality cascades are a series of duality transformations in field theories, which can be realized as the Hanany–Witten transitions brane configurations on circle. In setup Aharony–Bergman–Jafferis–Maldacena theory and its generalizations, from physical requirement that always end final destination depends only initial configuration, we propose fundamental domain supersymmetric tile whole parameter space relative ranks by translations, hence is parallelotope. We provide our arguments for proposal.