Unravelling T-Duality: Magnetic Quivers in Rank-zero Little String Theories

An intriguing class of 6d supersymmetric theories are known as little strings theories, which exhibit a rich network of T-dualities. A robust feature of these theories are their Higgs branches. Focusing on the little string theories that are realised on a single curve of zero self-intersection, we utilise brane systems to derive the magnetic quivers. Using a variety of techniques (including branching rules, brane dynamics, F-theory geometry, quiver subtraction, and the decay and fission algorithm), we detail the Higgs branch Hasse diagram and determine the transverse slices for every elementary Higgs branch RG-flow. Building on these insights, we pursue two directions: firstly, we used the established connection between the change of the 2-Group structure constants along Higgs branch RG-flows and the transition-type in the Hasse diagram to infer putative T-dual models. Secondly, we conjecture an algorithm that predicts the non-Abelian flavour symmetry of the compactified little string theory by inspecting the magnetic quivers of all T-dual frames.