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

2013/07/19 by Margarita García Pérez, Margarita Garcı́a Pérez, Antonio González-Arroyo +5 · 6 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #Gauge theory #Geometry #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Lambda #Lattice (music) #Mathematical physics #Mathematics #Monte Carlo method #Perturbation theory (quantum mechanics) #Physics #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Quantum Monte Carlo #Quantum mechanics #Scaling #String theory #Torus #Yang–Mills theory #hep-lat #hep-th

paper · pdf · doi:10.48550/arxiv.1307.5254

published in arXiv (Cornell University) (Cornell University) · 62 pages, 7 figures

arxiv created 2013/07/19 · openalex publication_date 2013/07/19 · arxiv updated 2013/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

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.

Citations

• The closed string spectrum of SU(N) gauge theories in 2+1 dimensions
• Computation of the string tension in four-dimensional Yang–Mills theory using large N reduction
• The Hamiltonian approach to Yang–Mills (2+1): Expansion scheme and corrections to string tension

Related

• Volume dependence in 2+1 Yang-Mills theory
• Perturbative analysis of twisted volume reduced theories
• A T₂ × R² roadmap to Confinement in SU(2) Yang-Mills theory
• The SU(N) running coupling in the twisted gradient flow scheme and volume independence
• Glueball masses in 2+1 dimensional SU(N) gauge theories with twisted boundary conditions