Static forces in gauge theories

Abstract

Using a three-level algorithm we perform a high-precision lattice computation of the static force up to 1fm in the 2+1 dimensional SU(5) gauge theory. Discretization errors and the continuum limit are discussed in detail. By comparison with existing SU(2) and SU(3) data it is found that σr 2 0 = 1.65 − π 24 holds at an accuracy of 1% for all N ≥ 2, where r 0 is the Sommer reference scale. The effective central charge c(r) is obtained and an intermediate distance r s is defined via the property c(r s ) = π 24 . It separates in a natural way the short-distance regime governed by perturbation theory from the long-distance regime described by an effective string theory. The ratio r s /r 0 decreases significantly from SU(2) to SU(3) to SU(5), where r s < r 0 . We give a preliminary estimate of its value in the large-N limit. The static force in the smallest representation of N -ality 2, which tends to the k = 2 string tension as r → ∞, is also computed up to 0.7fm. The deviation from Casimir scaling is positive and grows from 0.1% to 1% in that range.

Subleading properties of the QCD flux-tube in 3-d lattice gauge theory

“…For SU(3) on coarsest lattices [9] it is about 1.8r 0 . Similar indications are also there for SU (5) [12]. However this scale shifts towards larger r as one approaches the continuum limit.…”

Effective string description of confining flux tubes

“…Since ∆E decreases with R −1 the problem becomes more severe for large R. To reduce contaminations, there are two approaches: (i) Optimizing the z=0.976 (21) β=2.5 √ σR for studies of open flux tube spectra. [102][103][104][105][106][107][108][109][110][111][112][113] Similar studies have also been performed in 3D U(1) 62, 114 and 3D Z 2 42, 115-120 gauge theories. Measurement of the energy levels of closed flux tubes have started only little later.…”

The closed string spectrum of SU(N) gauge theories in 2+1 dimensions

“…This can be a significant portion of the total energy when the flux tube is short, so it is not clear whether the deviations from the infinite length limit seen in the open channel (for example see [17] and reference within) are due to this Coulomb interaction or whether they reflect string interactions. Our calculation, however, is free of this contamination simply because we study closed flux-tubes and by construction these do not have static charges and a Coulomb interaction.…”

“…The fit in Eq. (4.1) is the one usually performed (see for example [23]) and is the analog of the effective central charge fits performed in the open channel [4,17,24]. In contrast, the ansatz in Eq.…”