Superbosonisation via Riesz superdistributions
Alexander Alldridge, Zain Shaikh
TL;DR
This paper introduces a super-generalisation of the Riesz distribution to provide a new, conceptual proof of the superbosonisation identity, enhancing tools for studying universality in random matrix ensembles via supersymmetry.
Contribution
It identifies the superbosonisation identity's right-hand side with a super Riesz distribution and offers a new proof using harmonic superanalysis.
Findings
Superbosonisation identity linked to super Riesz distribution.
New proof of the identity using Laplace transform and harmonic superanalysis.
Enhanced understanding of supersymmetry methods in random matrix theory.
Abstract
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.
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