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

Abstract

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.

Recent progress in the effective string theory description of LGTs.

“…A similar analysis can be performed for the the effective string spectrum [15]. Also in this case, for the majority of the states, a good agreement with lattice simulations was found [16,17].…”

The deconfining phase transition of SO(N) gauge theories in 2+1 dimensions

“…We expect that E(l) → σl for l large [12]. For finite l, we expect E(l) to be well-approximated by [31][32][33][34] …”

SO(N) gauge theories in 2 + 1 dimensions: glueball spectra and confinement

“…(See e.g. [24,[44][45][46][47] and references therein.) We shall provide some checks for SO(N ) in section 4.…”

“…There will also be contributions with other quantum numbers, but these will require at least one of the flux tubes to be in an excited state. These are much heavier [24,[44][45][46][47] and so we assume they will not affect our calculations in this paper. An important remark is that since the 2 + and 2 − glueball spectra are identical in the continuum limit in an infinite volume, and since the low-lying 2 − spectrum is unaffected by torelons, a comparison between the two spectra at a finite but small lattice spacing provides a good tool for identifying those 2 + states which are affected by torelons.…”