Superbosonisation via Riesz superdistributions

The superbosonisation identity of Littelmann-Sommers-Zirnbauer is a new tool to study universality of random matrix ensembles via supersymmetry, which is applicable to non-Gaussian invariant distributions. In this note, we identify the right-hand side with a super-generalisation of the Riesz distribution. Using the Laplace transformation and tools from harmonic superanalysis, we give a short and conceptual new proof of the formula.