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

Scaling relations for the entire spectrum in mass-deformed conformal gauge theories

We consider mass-deformed conformal gauge theories (mCGT) and investigate the scaling behaviour of hadronic observables as a function of the fermion mass. Applying renormalization group arguments directly to matrix elements, we find m_H ~ m^{1/(1+gamma*)} and F ~ m^{\eta_F(gamma*)} for the decay constants, thereby generalizing our results from a previous paper to the entire spectrum. We derive the scaling law m_H \~m^{1/(1+gamma*)} using the Hellmann-Feynman theorem, and thus provide a derivation which does not rely on renormalization group arguments. Using the new results we reiterate, on the phenomenologically important, S-parameter. Finally, we discuss how spectral representations can be used to relate the mass and decay constant trajectories.Comment: 11 pages; typos removed, additional comments, version to appear in PL

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

An Overview of Lattice Results for Parton Distribution Functions

Following a ground-breaking proposal by Ji~\cite{PhysRevLett.110.262002}, numerical simulations of Quantum Chromo Dynamics (QCD) on a Euclidean lattice have provided new, valuable information on the structure of hadrons. In this talk, we briefly review the lattice approach to the reconstruction of parton densities, highlighting the connection between lattice observables and parton densities, with a focus on theoretical issues. Since parton distributions are extracted from lattice data by solving an inverse problem, we discuss some of the difficulties that affect these determinations and how they can be formulated in a Bayesian framework.Comment: 12 pages, 9 figures, contributed talk at the ISMD2022 conference, Pitlochry, Scotland. Minor typos corrected for publication in the proceedings of the conferenc

k-string tensions in the 4-d SU(N)-inspired dual Abelian-Higgs-type theory

The k-string tensions are explored in the 4-d $[U(1)]^{N-1}$-invariant dual Abelian-Higgs-type theory. In the London limit of this theory, the Casimir scaling is found in the approximation when small-sized closed dual strings are disregarded. When these strings are treated in the dilute-plasma approximation, explicit corrections to the Casimir scaling are found. The leading correction due to the deviation from the London limit is also derived. Its N-ality dependence turns out to be the same as that of the first non-trivial correction produced by closed strings. It also turns out that this N-ality dependence coincides with that of the leading correction to the k-string tension, which emerges by way of the non-diluteness of the monopole plasma in the 3-d SU(N) Georgi-Glashow model. Finally, we prove that, in the latter model, Casimir scaling holds even at monopole densities close to the mean one, provided the string world sheet is flat.Comment: 21 pages, no figures, uses JHEP3.cl

SU(N) gauge theories in the presence of a topological term

We review recent results on the theta dependence of the ground-state energy and spectrum of four-dimensional SU(N) gauge theories, where theta is the coefficient of the CP-violating topological term F-Fdual in the Lagrangian. In particular, we discuss the results obtained by Monte Carlo simulations of the lattice formulation of QCD, which allow the investigation of theta dependence around theta=0 by determining the moments of the topological charge distribution, and their correlations with other observables. The results for N=3 and larger values of N support the scenario obtained by general large-N scaling arguments.Comment: 18 pages, presentation at the HEP2007 Conference, Manchester, 7/2007. A couple of references adde

Anomalous dimensions of four-fermion operators from conformal EWSB dynamics

(Quasi)conformal scaling of composite operators from a strongly coupled EWSB dynamics helps to produce the characteristic hierarchies exhibited by the flavour couplings of the SM. It is however crucial to ensure that specific models satisfy bounds on Higgs and flavour dynamics; this in turn requires to control not only the anomalous dimensions of bilinears, but also those of higher-dimensional operators. We report on an ongoing effort to determine four-fermion operator anomalous dimensions, via Schr\"odinger Functional techniques, in the benchmark scenario of Minimal Walking Technicolour.Comment: 7 pages, 2 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

Fermions in higher representations. Some results about SU(2) with adjoint fermions

We discuss the lattice formulation of gauge theories with fermions in arbitrary representations of the color group, and present the implementation of the RHMC algorithm for simulating dynamical Wilson fermions. A first dataset is presented for the SU(2) gauge theory with two fermions in the adjoint representation, which has been proposed as a possible technicolor candidate. Simulations are performed on 8^3x16 lattices, at fixed lattice spacing. The PCAC mass, the pseudoscalar, vector and axial meson masses, the pseudoscalar meson decay constant are computed. The extrapolation to the chiral limit is discussed. However more extensive investigations are needed in order to control the systematic errors in the numerical results, and then understand in detail the phase structure of these theories.Comment: 7 pages, 3 figures. Talk presented at the XXVI International Symposium on Lattice Field Theory, July 14-19, 2008, Williamsburg, VA, US

Light scalar spectrum in extra-dimensional gauge theories

The phase diagram of five-dimensional SU(2) gauge theories with one compactified dimension on anisotropic lattices has a rich structure. In this contribution we show how to control non-perturbatively the scale hierarchy between the cut-off and the compactification scale in the bare parameter space. There exists a set of strong bare couplings where the the five-dimensional lattice theory can be described by an effective four-dimensional theory with a scalar field in the adjoint representation. We present a detailed study of the light scalar spectrum as it arises from the non-perturbative dynamics of the full five-dimensional lattice theory. We also investigate the mixing with scalar glueball states in the attempt to further establish the extra-dimensional nature of light scalar states.Comment: 7 pages, 4 figures. To appear in the proceedings of the 30th International Symposium on Lattice Field Theory, June 24-29 201