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 × l with twisted boundary conditions. This paper extends our previous work [1]. 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 = λN l/(4π) (with λ 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.
Highlights
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 = λN l/(4π) and the twist angle θdefined in terms of the magnetic flux piercing the two-dimensional box
The present paper extends our previous study [1,2,3] on the behaviour of pure SU(N) YangMills theory in 2+1 dimensions, where space is compactified as a 2-dimensional torus with ’t Hooft twisted boundary conditions
We focus upon the dependence of the spectrum of the theory on the parameters that define it, namely the torus size l, the number of colours N, and the magnetic flux k introduced by the boundary conditions
Summary
The present paper extends our previous study [1,2,3] on the behaviour of pure SU(N) YangMills theory in 2+1 dimensions, where space is compactified as a 2-dimensional torus with ’t Hooft twisted boundary conditions. Twisted boundary condition on a torus were introduced by ’t Hooft [30, 31] as a way to induce topological (chromo-) electric and magnetic fluxes in Yang-Mills theories This is best understood in the Hamiltonian formalism in the A0 = 0 gauge. As mentioned in the introduction, the purpose of this paper is to present the results of a non-perturbative analysis of the volume and N dependence of the spectrum in the different sectors, extending to the zero electric flux sector the results obtained in ref. We will present the results of our study of the spectrum separating the cases of non-vanishing and vanishing electric flux
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