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

Detecting Dual Superconductivity in the Ground State of Gauge Theory

We explicitly construct a monopole creation operator: its vacuum expectation value is an order parameter for dual superconductivity, in that, if different from zero, it signals a spontaneous breaking of the $U(1)$ symmetry corresponding to monopole charge conservation. This operator is tested by numerical simulations in compact $U(1)$ gauge theory. Our construction provides a general recipe for detection of the condensation of any topological soliton. In particular our operator can be used to detect dual superconductivity of the QCD vacuum.Comment: 10 pages, 3 figures avalaible on request. REVTE

Chiral symmetry breaking in the 3-d Thirring model for small NfN_f

We study the dynamical breaking of chiral symmetry in the 3-d Thirring model for a small number of fermion species. The critical point is identified by fitting lattice data to an equation of state. The spectrum of the theory is studied to confirm the phase structure of the model.Comment: 3 pages, 3 figures. Talk presented at Lattice '9

The phase structure of the 3-d Thirring model

We study the phase structure of the Thirring model in 3-d and find it to be compatible with the existence of a non gaussian fixed point of RG. A Finite Size Scaling argument is included in the equation of state in order to avoid the assumptions usually needed to extrapolate to the thermodynamical limit.Comment: Talk presented at LATTICE96(other models

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

The SU(2) Confining Vacuum as a Dual Superconductor

We investigate the dual superconductivity hypothesis in pure SU(2) lattice gauge theory. We find evidence of the dual Meissner effect both in the maximally Abelian gauge and without gauge fixing. We also obtain a rather good extimation of the string tension using the value of the London penetration length.Comment: 4 pages, uuencoded compressed (using GNU's gzip) tar file containing 1 LaTeX2e file, 5 encapsulated Postscript figures, and espcrc2.sty. Contribution to Lattice 9

Topological susceptibility for the SU(3) Yang--Mills theory

We present the results of a computation of the topological susceptibility in the SU(3) Yang--Mills theory performed 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 \pm 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: Talk presented at Lattice2004(topology); 3 pages, 2 figure

k-string tensions in the 3-d SU(N) Georgi-Glashow model

The classic argument by Polyakov showing that monopoles produce confinement in the Higgs phase of the Georgi-Glashow model is generalized to study the spectrum of k-strings. We find that the leading-order low-density approximation yields Casimir scaling in the weakly-coupled 3-d SU(N) Georgi-Glashow model. Corrections to the Casimir formula are considered. When k is of the order of N, the non-diluteness effect is of the same order as the leading term, indicating that non-diluteness can significantly change the Casimir-scaling behavior. The correction produced by the propagating Higgs field is also studied and found to increase, together with the non-diluteness effect, the Casimir-scaling ratio. Furthermore, a correction due to closed k-strings is also computed and is shown to yield the same k-dependence as the one due to non-diluteness, but with the opposite sign and a nontrivial N-dependence. Finally, we consider the possible implications of our analysis for the SU(N) analogue of compact QED in four dimensions.Comment: 17 pages, no figures, uses JHEP3.cl

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

Some Insights into the Method of Center Projection

We present several new results which pertain to the successes of center projection in maximal center gauge (MCG). In particular, we show why any center vortex, inserted "by hand" into a thermalized lattice configuration, will be among the set of vortices found by the center projection procedure. We show that this "vortex-finding property" is lost when gauge-field configurations are fixed to Landau gauge prior to the maximal center gauge fixing; this fact accounts for the loss of center dominance in the corresponding projected configurations. Variants of maximal center (adjoint Landau) gauge are proposed which correctly identify relevant center vortices.Comment: LATTICE99(confine), 3 pages, 3 figure