Spatial volume dependence for 2+1 dimensional SU(N) Yang-Mills theory

We study the 2+1 dimensional SU(N) Yang-Mills theory on a finite two-torus with twisted boundary conditions. Our goal is to study the interplay between the rank of the group N , the length of the torus L and the Z ( )N( ) magnetic flux. After presenting the classical and quantum formalism, we analyze the spectrum of the theory using perturbation theory to one-loop and using Monte Carlo techniques on the lattice. In perturbation theory, results to all orders depend on the combination x = λN L and an angle defined in terms of the magnetic flux (λ is ‘t Hooft coupling). Thus, fixing the angle, the system exhibits a form of volume independence (N L dependence). The numerical results interpolate between our perturbative calculations and the confinement regime. They are consistent with x-scaling and provide interesting information about the k-string spectrum and effective string theories. The occurrence of tachyonic instabilities is also analysed. They seem to be avoidable in the large N limit with a suitable scaling of the magnetic flux.

Note:

62 pages, 7 figures

flux: magnetic
gauge field theory: Yang-Mills
boundary condition: twist
tachyon: stability
perturbation theory
gauge field theory: SU(N)
expansion 1/N
string model
confinement
numerical calculations: Monte Carlo

References(0)

Figures(0)

Loading ...