$\theta$ Vacuum in a Random Matrix Model

TL;DR

This paper models the $ heta$-vacuum using a Gaussian matrix model inspired by lattice calculations, revealing a cusp in vacuum energy at $ heta< ext{pi}$ that depends on numerical accuracy and winding mode density.

Contribution

It introduces a matrix model approach to study the $ heta$-vacuum, capturing key features observed in lattice simulations.

Findings

Vacuum energy shows a cusp at $ heta< ext{pi}$.

Cusp sensitivity depends on numerical precision.

Winding mode density influences the vacuum structure.

Abstract

Inspired by recent lattice calculations, we model certain aspects of the $\theta$-vacuum using a matrix model with gaussian weights. The vacuum energy exhibits a cusp at $\theta <\pi$ that is sensitive to both the accuracy of the numerical analysis and the maximum density of winding modes present in a finite volume.