Biagio Lucini

SU(N) gauge theories at large N

We review the theoretical developments and conceptual advances that stemmed from the generalization of QCD to the limit of a large number of color charges, originally proposed by ’t Hooft. Then, after introducing the gauge-invariant non-perturbative formulation of non-Abelian gauge theories on a spacetime lattice, we present a selection of results from recent lattice studies of theories with a dierent number of colors, and the ndings obtained from their extrapolation to the ’t Hooft limit. We conclude with a brief discussion and a summary.

The high temperature phase transition in SU(N) gauge theories

We calculate the continuum value of the deconfining temperature in units of the string tension for SU(4), SU(6) and SU(8) gauge theories, and we recalculate its value for SU(2) and SU(3). We find that the N-dependence for 2 ≤ N ≤ 8 is well fitted by Tc/√σ = 0.596(4)+0.453(30)/N2, showing a rapid convergence to the large-N limit. We confirm our earlier result that the phase transition is first order for N ≥ 3 and that it becomes stronger with increasing N. We also confirm that as N increases the finite volume corrections become rapidly smaller and the phase transition becomes visible on ever smaller volumes. We interpret the latter as being due to the fact that the tension of the domain wall that separates the confining and deconfining phases increases rapidly with N. We speculate on the connection to Eguchi-Kawai reduction and to the idea of a Master Field.

Color confinement and dual superconductivity of the vacuum. IV

SUMMARY A scaling analysis is made of the order parameter describing monopole condensation at the deconfining transition of N_f=2 QCD around the chiral point. In accordance with scaling properties of the specific heat, studied in a previous paper, scaling is consistent with a first order transition. The status of dual superconductivity of the vacuum as a mechanism of color confinement is reviewed.

The deconfinement transition in SU(N) gauge theories

Abstract We investigate the properties of the deconfinement transition in SU(4) and SU(6) gauge theories. We find that it is a ‘normal’ first order transition in both cases, from which we conclude that the transition is first order in the N→∞ limit. Comparing our preliminary estimates of the continuum values of T c / σ with existing values for SU(2) and SU(3) demonstrates a weak dependence on N for all values of N.

The k=2 string tension in four-dimensional SU(N) gauge theories

Abstract We calculate the k =2 string tension in SU (4) and SU (5) gauge theories in 3+1 dimensions, and compare it to the k =1 fundamental string tension. We find, from the continuum extrapolation of our lattice calculations, that σ k =2 / σ f =1.40±0.08 in the SU (4) gauge theory, and that σ k =2 / σ f =1.56±0.10 in SU (5). We remark upon the way this might constrain the dynamics of confinement and the intriguing implications it might have for the mass spectrum of SU ( N ) gauge theories. We also note that these results agree closely with the MQCD-inspired conjecture that the SU ( N ) string tension varies as σ k ∝ sin( πk / N ).

Evidence for Diquarks in Lattice QCD

Diquarks may play an important role in hadron spectroscopy, baryon decays, and color superconductivity. We investigate the existence of diquark correlations in lattice QCD by considering systematically all the lowest energy diquark channels in a color gauge-invariant setup. We measure mass differences between the various channels and show that the positive parity scalar diquark is the lightest. Quark-quark correlations inside the diquark are clearly seen in this channel, and yield a diquark size of O(1) fm.

G_2 gauge theory at finite temperature

The gauge group being centreless, G2 gauge theory is a good laboratory for studying the role of the centre of the group for colour confinement in Yang-Mills gauge theories. In this paper, we investigate G2 pure gauge theory at finite temperature on the lattice. By studying the finite size scaling of the plaquette, the Polyakov loop and their susceptibilities, we show that a deconfinement phase transition takes place. The analysis of the pseudocritical exponents give strong evidence of the deconfinement transition being first order. Implications of our findings for scenarios of colour confinement are discussed.

SU(Nc) gauge theories at deconfinement

Abstract The deconfinement transition in SU ( N c ) Yang–Mills is investigated by Monte Carlo simulations of the gauge theory discretized on a spacetime lattice. We present new results for 4 ⩽ N c ⩽ 8 (in particular, for N c = 5 and N c = 7 ), which are analysed together with previously published results. The increased amount of data, the improved statistics and simulations closer to the continuum limit provide us with better control over systematic errors. After performing the thermodynamic limit, numerical results for the ratio of the critical temperature T c over the square root of the string tension σ obtained on lattices with temporal extensions N t = 5 , 6 , 7 , 8 are extrapolated to the continuum limit. The continuum results at fixed N c are then extrapolated to N c = ∞ . We find that our data are accurately described by the formula T c / σ = 0.5949 ( 17 ) + 0.458 ( 18 ) / N c 2 . Possible systematic errors affecting our calculations are also discussed.

Introductory lectures to large-N QCD phenomenology and lattice results

An elementary, pedagogical introduction to the large-N limit of QCD and to its phenomenological implications is presented, and a survey of lattice results in the ’t Hooft limit is briefly discussed.

Color confinement and dual superconductivity in full QCD

SUMMARY We report on evidence that confinement is related to dual superconductivity of the vacuum in full QCD, as in quenched QCD. The vacuum is a dual superconductor in the confining phase, whilst the U(1) magnetic symmetry is realized a la Wigner in the deconfined phase.