Large N and confining flux tubes as strings - A view from the lattice
Acta Physica Polonica B 40:12 (2009) 3249-3320
Abstract:
I begin this paper by describing some of the useful things that we have learned about large-N gauge theories using lattice simulations. For example that the theory is confining in that limit, that for many quantities SU(3) ≃ SU(∞), and that this includes the strongly coupled gluon plasma just above Tc, thus providing some justification for the use of gauge-gravity duality in analysing QCD at RHIC/LHC temperatures. I then turn, in a more detailed discussion, to recent progress on the problem of what effective string theory describes confining flux tubes. I describe lattice calculations of the energy spectrum of closed loops of confining flux, and some dramatic analytic progress in extending the 'universal Luscher correction' to terms that are of higher order in 1=l2, where l is the length of the string. Both approaches point increasingly to the Nambu-Goto free string theory as being the appropriate starting point for describing string-like degrees of freedom in SU(N) gauge theories.On the spectrum of closed k = 2 flux tubes in D=2+1 SU (N) gauge theories
Journal of High Energy Physics 2009:5 (2009)
Abstract:
We calculate the energy spectrum of a k = 2 flux tube that is closed around a spatial torus, as a function of its length l. We do so for SU(4) and SU(5) gauge theories in 2 space dimensions. We find that to a very good approximation the eigenstates belong to the irreducible representations of the SU(N) group rather than just to its center, Z N. We obtain convincing evidence that the low-lying states are, for l not too small, very close to those of the Nambu-Goto free string theory (in flat space-time). The correction terms appear to be typically of O(1) in appropriate units, much as one would expect if the bosonic string model were an effective string theory for the dynamics of these flux tubes. This is in marked contrast to the case of fundamental flux tubes where such corrections have been found to be unnaturally small. Moreover we find that these corrections appear to be particularly small when the 'phonons' along the string have the same momentum, and large when their momentum is opposite. This provides information about the detailed nature of the interactions in the effective string theory. We have searched for, but not found, extra states that would arise from the excitation of the massive modes presumably associated with the non-trivial structure of the flux tube. © 2009 SISSA.The spectrum of closed loops of fundamental flux in D = 3+1 SU(N) gauge theories
Proceedings of Science 91 (2009)
Abstract:
We study the spectrum of closed flux tubes in four dimensional SU(N) gauge theories. We do so by calculating the energies of the low lying states with the variational technique (whose basis consists of about 700 operators). We study states of different values of angular momentum, transversal parity, longitudinal parity, and longitudinal momentum, and compare the results with effective string theories (ESTs) such as the Nambu-Goto (NG) model. Most of our states agree very well with the Nambu-Goto predictions and since most of our flux-tubes' lengths are outside the radius of convergence of the ESTs, then for some states it is only the NG that predicts the spectrum well. This strongly suggests that the ESTs can be re-summed. Nonetheless, there are a few states (all with negative parity and in the same representation of the lattice rotation group) that exhibit large deviations from the NG predictions; these deviations might provide clues to the nature of the effective string theory describing the large-N QCD string.On the running of the bare coupling in SU(N) lattice gauge theories
Journal of High Energy Physics 2008:7 (2008)
Abstract:
Interpreting the way that the SU(3) bare lattice coupling runs with the lattice spacing is complicated by the fact that there is a smooth cross-over region in which the strong coupling expansion transforms into a weak-coupling one. For N 5, however, there is a first order bulk transition that cleanly separates the strong and weak coupling regimes. We find that in this case the calculated string tension can be readily fitted throughout the weak coupling region by a standard 3-loop expression modified by lattice spacing corrections of the expected form. While our fits demand the presence of the latter, they do not constrain the perturbative coupling scheme enough to enable us to extract a usefully accurate value of a(β) in units of Λ MS. To resolve this ambiguity we turn to SU(3) where we use the Schrodinger Functional coupling scheme to extract a value of r 0Λ SF as a benchmark. We then find that the Parisi mean-field improved coupling scheme closely reproduces this result. We also develop a comparison between different schemes that does not rely on the calculation of any physical quantity and which can therefore be applied much further into weak coupling. Again the Parisi scheme is favoured over the others that we compare. Using the mean-field scheme we have fitted the values of the string tension a 2σ that have been calculated for 2 N 8, to obtain Λ MS/σ = 0.503(2)(40)+0.33(3)(3)/N 2 for N 3, where the first error is statistical and the second is our estimate of the systematic error from all sources.Closed k-strings in SU(N) gauge theories: 2 + 1 dimensions
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 663:5 (2008) 429-437