Abstract:We calculate the energy spectrum of a confining flux tube that is closed around a spatial torus, as a function of its length l. We do so for various SU(N ) gauge theories in 3+1 dimensions, and for various values of spin, parity and longitudinal momentum. We are able to present usefully accurate results for about 20 of the lightest such states, for a range of l that begins close to the (finite volume) deconfining phase transition at l √ σ ∼ 1.6, and extends up to l √ σ ∼ 6 (where σ is the string tension). We find that most of these low-lying states are well described by the spectrum of the Nambu-Goto free string theory in flat space-time. Remarkably, this is so not only at the larger values of l, where the gap between the ground state energy and the low-lying excitations becomes small compared to the mass gap, but also down to much shorter lengths where these excitation energies become large compared to √ σ, the flux-tube no longer 'looks' anything like a thin string, and an expansion of the effective string action in powers of 1/l no longer converges. All this is for flux in the fundamental representation. We also calculate the k = 2 (anti)symmetric ground states and these show larger corrections at small l. So far all this closely resembles our earlier findings in 2+1 dimensions. However, and in contrast to the situation in D = 2+1, we also find that there are some states, with J P = 0 − quantum numbers, that show large deviations from the Nambu-Goto spectrum. We investigate the possibility that (some of) these states may encode the massive modes associated with the internal structure of the flux tube, and we discuss how the precocious free string behaviour of most states constrains the effective string action, on which much interesting theoretical progress has recently been made.

We report on new results on the infrared behavior of the three-gluon vertex in quenched Quantum Chromodynamics, obtained from large-volume lattice simulations. The main focus of our study is the appearance of the characteristic infrared feature known as ‘zero crossing’, the origin of which is intimately connected with the nonperturbative masslessness of the Faddeev–Popov ghost. The appearance of this effect is clearly visible in one of the two kinematic configurations analyzed, and its theoretical origin is discussed in the framework of Schwinger–Dyson equations. The effective coupling in the momentum subtraction scheme that corresponds to the three-gluon vertex is constructed, revealing the vanishing of the effective interaction at the exact location of the zero crossing.The research of J.P. and J.R-Q is supported by the Spanish MINECO under grant FPA2014-53631-C2-1-P and FPA2014-53631-C2-2-P and SEV-2014-0398, and Generalitat Valenciana under grant Prometeo II/2014/066. S. Z. acknowledges support by the Alexander von Humboldt Foundation. We thank K. Cichy, M. Creutz, O. Pene, O. Philipsen, M. Teper, J. Verbaarschot for fruitful discussions. Numerical computations have used resources of CINES and GENCI-IDRIS as well as resources at the IN2P3 computing facility in Lyon

We calculate the low-lying glueball spectrum and various string tensions in SU(N ) lattice gauge theories in 2 + 1 dimensions, and extrapolate the results to the continuum limit. We do so for for the range N ∈ [2, 16] so as to control the N -dependence with a useful precision. We observe a number of striking near-degeneracies in the various J P C sectors of the glueball spectrum, in particular between C = + and C = − states. We calculate the string tensions of flux tubes in a number of representations, and provide evidence that the leading correction to the N -dependence of the k-string tensions is ∝ 1/N rather than ∝ 1/N 2 , and that the dominant binding of k fundamental flux tubes into a kstring is via pairwise interactions. We comment on the possible implications of our results for the dynamics of these gauge theories.

SU(2) gauge theory with one Dirac flavour in the adjoint representation is investigated on a lattice. Initial results for the gluonic and mesonic spectrum, static potential from Wilson and Polyakov loops, and the anomalous dimension of the fermionic condensate from the Dirac mode number are presented. The results found are not consistent with conventional confining behaviour, instead tentatively pointing towards a theory lying within or very near the onset of the conformal window, with the anomalous dimension of the fermionic condensate in the range 0.9 < ∼ γ * < ∼ 0.95. The implications of our work for building a viable theory of strongly interacting dynamics beyond the standard model are discussed.