Colour confinement and dual superconductivity of the vacuum - I

We study dual superconductivity of the ground state of SU(2) gauge theory, in connection with confinement. We do that measuring on the lattice a disorder parameter describing condensation of monopoles. Confinement appears as a transition to dual superconductor, independent of the abelian projection defining monopoles. Some speculations are made on the existence of a more appropriate disorder parameter. A similar study for SU(3) is presented in a companion paper.Comment: Some typos corrected, acknowledgements added; to appear on Phys. Rev.

Glueball masses in the large N limit

The lowest-lying glueball masses are computed in SU($N$) gauge theory on a spacetime lattice for constant value of the lattice spacing $a$ and for $N$ ranging from 3 to 8. The lattice spacing is fixed using the deconfinement temperature at temporal extension of the lattice $N_T = 6$. The calculation is conducted employing in each channel a variational ansatz performed on a large basis of operators that includes also torelon and (for the lightest states) scattering trial functions. This basis is constructed using an automatic algorithm that allows us to build operators of any size and shape in any irreducible representation of the cubic group. A good signal is extracted for the ground state and the first excitation in several symmetry channels. It is shown that all the observed states are well described by their large $N$ values, with modest ${\cal O}(1/N^2)$ corrections. In addition spurious states are identified that couple to torelon and scattering operators. As a byproduct of our calculation, the critical couplings for the deconfinement phase transition for N=5 and N=7 and temporal extension of the lattice $N_T=6$ are determined.Comment: 1+36 pages, 22 tables, 21 figures. Typos corrected, conclusions unchanged, matches the published versio

Free energy and theta dependence of SU(N) gauge theories

We study the dependence of the free energy on the CP violating angle theta, in four-dimensional SU(N) gauge theories with N >= 3, and in the large-N limit. Using the Wilson lattice formulation for numerical simulations, we compute the first few terms of the expansion of the ground-state energy F(theta) around theta = 0, F(theta) - F(0) = A_2 theta^2 (1 + b_2 theta^2 + ...). Our results support Witten's conjecture: F(theta) - F(0) = A theta^2 + O(1/N) for theta < pi. We verify that the topological susceptibility has a nonzero large-N limit chi_infinity = 2A with corrections of O(1/N^2), in substantial agreement with the Witten-Veneziano formula which relates chi_infinity to the eta' mass. Furthermore, higher order terms in theta are suppressed; in particular, the O(theta^4) term b_2 (related to the eta' - eta' elastic scattering amplitude) turns out to be quite small: b_2 = -0.023(7) for N=3, and its absolute value decreases with increasing N, consistently with the expectation b_2 = O(1/N^2).Comment: 3 pages, talk presented at the conference Lattice2002(topology). v2: One reference has been updated, no further change

Topological susceptibility of SU(N) gauge theories at finite temperature

We investigate the large-N behavior of the topological susceptibility in four-dimensional SU(N) gauge theories at finite temperature, and in particular across the finite-temperature transition at Tc. For this purpose, we consider the lattice formulation of the SU(N) gauge theories and perform Monte Carlo simulations for N=4,6. The results indicate that the topological susceptibility has a nonvanishing large-N limit for T<Tc, as at T=0, and that the topological properties remain substantially unchanged in the low-temperature phase. On the other hand, above the deconfinement phase transition, the topological susceptibility shows a large suppression. The comparison between the data for N=4 and N=6 hints at a vanishing large-N limit for T>Tc.Comment: 9 pages, 2 figs, a few discussions added, JHEP in pres

Topological susceptibility in the SU(3) gauge theory

We compute the topological susceptibility for the SU(3) Yang--Mills theory by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r_0^4 chi = 0.059(3), which corresponds to chi=(191 +/- 5 MeV)^4 if F_K is used to set the scale. Our result supports the Witten--Veneziano explanation for the large mass of the eta'.Comment: Final version to appear on Phys. Rev. Let

Conformal vs confining scenario in SU(2) with adjoint fermions

The masses of the lowest-lying states in the meson and in the gluonic sector of an SU(2) gauge theory with two Dirac flavors in the adjoint representation are measured on the lattice at a fixed value of the lattice coupling $\beta = 4/g_0^2 = 2.25$ for values of the bare fermion mass $m_0$ that span a range between the quenched regime and the massless limit, and for various lattice volumes. Even for light constituent fermions the lightest glueballs are found to be lighter than the lightest mesons. Moreover, the string tension between two static fundamental sources strongly depends on the mass of the dynamical fermions and becomes of the order of the inverse squared lattice linear size before the chiral limit is reached. The implications of these findings for the phase of the theory in the massless limit are discussed and a strategy for discriminating between the (near--)conformal and the confining scenario is outlined.Comment: 5 pages, 4 figures using RevTeX4, Typos corrected, references added. Versions to appear on PR

Analyticity in theta on the lattice and the large volume limit of the topological susceptibility

Non-analyticity of QCD with a \theta term at \theta=0 may signal a spontaneous breaking of both parity and time reversal invariance. We address this issue by investigating the large volume limit of the topological susceptibility $\chi$ in pure SU(3) gauge theory. We obtain an upper bound for the symmetry breaking order parameter and, as a byproduct, the value \chi=(173.4(+/- 0.5)(+/- 1.2)(+1.1 / -0.2) MeV)^4 at \beta=6 (a approx= 0.1 fermi). The errors are the statistical error from our data, the one derived from the value used for \Lambda_L and an estimate of the systematic error respectively.Comment: 15 pages, corrected typos, added 1 reference, minor changes in tex

The decay of unstable k-strings in SU(N) gauge theories at zero and finite temperature

Sources in higher representations of SU(N) gauge theory at T=0 couple with apparently stable strings with tensions depending on the specific representation rather than on its N-ality. Similarly at the deconfining temperature these sources carry their own representation-dependent critical exponents. It is pointed out that in some instances one can evaluate exactly these exponents by fully exploiting the correspondence between the 2+1 dimensional critical gauge theory and the 2d conformal field theory in the same universality class. The emerging functional form of the Polyakov-line correlators suggests a similar form for Wilson loops in higher representations which helps in understanding the behaviour of unstable strings at T=0. A generalised Wilson loop in which along part of its trajectory a source is converted in a gauge invariant way into higher representations with same N-ality could be used as a tool to estimate the decay scale of the unstable strings.Comment: 18 pages, 4 figures v2: typos correcte