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arXiv · 1307.5254

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

Margarita García Pérez·Antonio González-Arroyo·Masanori Okawa
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Abstract

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=λNL 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 (NL 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.

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Margarita García Pérez, Antonio González-Arroyo, Masanori Okawa. 2013-07-19. Spatial volume dependence for 2+1 dimensional SU(N) Yang-Mills theory. https://arxiv.org/abs/1307.5254

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