Pfaffian Interaction and $BCD$-quiver Matrix Models

TL;DR

This paper explores Pfaffian interactions in matrix models, extending classical beta-ensembles, and introduces Pfaffian formulas for partition functions and characteristic polynomials, especially in BCD-type quiver models.

Contribution

It provides new Pfaffian formulas for matrix model partition functions and characteristic polynomial averages, generalizing standard beta=1 and 4 models to BCD-quiver structures.

Findings

Derived Pfaffian formulas for partition functions.

Extended matrix models to BCD-type quivers.

Connected Pfaffian interactions with classical ensembles.

Abstract

We study matrix models involving Pfaffian interactions as generalizations of the standard $\beta = 1$ and $\beta = 4$ matrix models. We present the Pfaffian formulas for the partition function and the characteristic polynomial averages. We also explore the matrix chain with the Pfaffian interaction, which realizes the BCD-type quiver matrix models.