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

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: $x=\lambda Nl/(4\pi )$ (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.

arXiv commentpdflatex 56 pages, 12 figures and 28 tables revised version with minor changes in text and tables

References in corpus (26)

• Noncommutative Field Theory
• Noncommutative Perturbative Dynamics
• On the generalized eigenvalue method for energies and matrix elements in lattice field theory
• SU(N) gauge theories in 2+1 dimensions
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Lattice Gauge Fields and Discrete Noncommutative Yang-Mills Theory
• Volume independence in large Nc QCD-like gauge theories
• Perturbative analysis on infrared and ultraviolet aspects of noncommutative QED on R^4
• Nonperturbative Dynamics of Noncommutative Gauge Theory
• Large N reduction in the continuum three dimensional Yang-Mills theory
• Constant contribution in meson correlators at finite temperature
• Large $N$ reduction with the Twisted Eguchi-Kawai model
• The string tension from smeared Wilson loops at large N
• A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability
• Symmetry Breaking In Twisted Eguchi-Kawai Models
• SU(N) gauge theories in 2+1 dimensions: glueball spectra and k-string tensions
• Phase structure of twisted Eguchi-Kawai model
• Large N Volume Independence and an Emergent Fermionic Symmetry
• Perturbative Instabilities on the Non-Commutative Torus, Morita Duality and Twisted Boundary Conditions
• Testing volume independence of SU(N) pure gauge theories at large N
• Morita Duality and Large-N Limits
• Aspects of Gauge Theory on Commutative and Noncommutative Tori
• Phases of three dimensional large N QCD on a continuum torus
• Tachyonic instabilities in 2+1 dimensional Yang-Mills theory and its connection to Number Theory
• On the short-distance structure of irrational non-commutative gauge theories
• Glueball masses in 2+1 dimensional SU(N) gauge theories with twisted boundary conditions

Cited by in corpus (5)

• SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology
• Tachyonic instabilities in 2+1 dimensional Yang-Mills theory and its connection to Number Theory
• The twisted gradient flow coupling at one loop
• Center-vortex semiclassics with non-minimal 't Hooft fluxes on ${\mathbb{R}}^2\times T^2$ and center stabilization at large $N$
• Memory efficient finite volume schemes with twisted boundary conditions