# Fermionic construction of partition function for multi-matrix models and multi-component TL hierarchy

## TL;DR

This paper develops a fermionic framework to represent multi-matrix models and explores their connections with multi-component integrable hierarchies, revealing new flows that extend standard matrix models.

## Contribution

It introduces a fermionic construction for multi-matrix models and links them to p-component KP and TL hierarchies, showing how to generate new matrix models through hierarchy flows.

## Key findings

- Fermionic representation of multi-matrix integrals.
- Connection between matrix models and p-component hierarchies.
- Identification of new flows transforming standard matrix models.

## Abstract

We use $p$-component fermions $(p=2,3,...)$ to present $(2p-2)N$-fold integrals as a fermionic expectation value. This yields fermionic representation for various $(2p-2)$-matrix models. Links with the $p$-component KP hierarchy and also with the $p$-component TL hierarchy are discussed. We show that the set of all (but two) flows of $p$-component TL changes standard matrix models to new ones.