The spectrum of 2+1 dimensional Yang-Mills theory on a twisted spatial torus

TL;DR

This paper analyzes the low-lying spectrum of 2+1 dimensional SU(N) Yang-Mills theory on a twisted torus, revealing key dependencies and implications for volume independence and non-commutative field theories.

Contribution

It provides a comprehensive non-perturbative analysis of the spectrum, extending previous work, and introduces a simple expression capturing the spectrum's dependence on key parameters.

Findings

Spectrum depends on parameters through x and twist angle

No tachyonic instabilities observed in the spectrum

Large-volume glueball states emerge at a fixed x value

Abstract

We compute and analyse the low-lying spectrum of 2+1 dimensional $SU(N)$ Yang-Mills theory on a spatial torus of size $l\times l$ with twisted boundary conditions. This paper extends our previous work \cite{Perez:2013dra}. In that paper we studied the sector with non-vanishing electric flux and concluded that the energies only depend on the parameters through two combinations: $x=\lambda N l /(4\pi)$ (with $\lambda$ the 't Hooft coupling) and the twist angle $\tilde \theta$ defined in terms of the magnetic flux piercing the two-dimensional box. Here we made a more complete study and we are able to condense our results, obtained by non-perturbative lattice methods, into a simple expression which has important implications for the absence of tachyonic instabilities, volume independence and non-commutative field theory. Then we extend our study to the sector of vanishing electric flux. We conclude that the onset of the would-be large-volume glueball states occurs at an approximately fixed value of $x$, much before the stringy torelon states have become very massive.