Closed flux tubes and their string description in D=2+1 SU(N) gauge theories

• Published in: The journal of high energy physics Vol. 2011; no. 5
• Main Authors: Athenodorou, Andreas, Bringoltz, Barak, Teper, Michael
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.05.2011; Springer Nature B.V
• Subjects: Classical and Quantum Gravitation; Elementary Particles; Excitation; Flux; High energy physics; Lattice vibration; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; String Theory; Strings; Toruses; Tubes; Confinement; 1/N Expansion; Lattice Gauge Field Theories; Bosonic Strings
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2011)042

We carry out lattice calculations of the spectrum of confining flux tubes that wind around a spatial torus of variable length l , in 2 + 1 dimensions. We compare the energies of the lowest ∼30 states to the free string Nambu-Goto model and to recent results on the universal properties of effective string actions. Our most useful calculations are in SU(6) at a small lattice spacing, which we check is very close to the N → ∞ continuum limit. We find that the energies, E n ( l ), are remarkably close to the predictions of the free string Nambu-Goto model, even well below the critical length at which the expansion of the Nambu-Goto energy in powers of 1/ l 2 diverges and the series needs to be resummed. Our analysis of the ground state supports the universality of the O (1/ l ) and the O (1/ l 3 ) corrections to σl , and we find that the deviations from Nambu-Goto at small l prefer a leading correction that is O (1/ l 7 ), consistent with theoretical expectations. We find that the low-lying states that contain a single phonon excitation are also consistent with the leading O (1/ l 7 ) correction dominating down to the smallest values of l . By contrast our analysis of the other light excited states clearly shows that for these states the corrections at smaller l resum to a much smaller effective power. Finally, and in contrast to our recent calculations in D = 3 + 1, we find no evidence for the presence of any non-stringy states that could indicate the excitation of massive flux tube modes.