On the vacuum wavefunction and string tension of Yang-Mills theories in (2+1) dimensions

TL;DR

This paper provides an analytical calculation of the vacuum wavefunction and string tension in (2+1)-dimensional Yang-Mills theories, aligning well with lattice results and covering different momentum regimes.

Contribution

It extends previous gauge-invariant matrix variable analysis to derive the vacuum wavefunction and string tension from first principles in (2+1) dimensions.

Findings

Vacuum wavefunction matches expected high and low momentum behavior.

String tension value agrees with recent lattice Monte Carlo results.

Analytical approach confirms numerical findings.

Abstract

We present an analytical continuum calculation, starting from first principles, of the vacuum wavefunction and string tension for pure Yang-Mills theories in $(2+1)$ dimensions, extending our previous analysis using gauge-invariant matrix variables. The vacuum wavefunction is consistent with what is expected at both high and low momentum regimes. The value of the string tension is in very good agreement with recent lattice Monte Carlo evaluations.