An equivalence in random matrix and tensor models via a dually weighted intermediate field representation

TL;DR

This paper introduces new equivalences between random matrix and tensor models using a dually weighted intermediate field representation, unifying complex and self-adjoint theories with potential implications for real tensor models.

Contribution

It develops a generalized intermediate field representation that reveals equivalences between complex and self-adjoint models, extending standard methods.

Findings

Partition functions of certain models are different integral representations of the same function.

Found new dually weighted intermediate field representations generalizing standard methods.

Indications of an equivalence between real tensor models and self-transpose tensor models.

Abstract

We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that the partition functions of certain self-adjoint models and their complex counterparts are different integral representations of the exact same function. A special case of these equivalences takes a form of newly found dually weighted intermediate field representations, which generalize the standard intermediate field representation. We also find indications of an equivalence between real tensor models and self-transpose tensor models.