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A detailed investigation of finite size effects is performed for SU(2) gauge theory with two fermions in the adjoint representation, which previous lattice studies have shown to be inside the conformal window. The system is investigated with different spatial and temporal boundary conditions on lattices of various spatial and temporal extensions, for two values of the bare fermion mass representing a {\em heavy} and {\em light} fermion regime. Our study shows that the infinite volume limit of masses and decay constants in the mesonic sector is reached only when the mass of the pseudoscalar particle $M_\mathrm{PS}$ and the spatial lattice size $L$ satisfy the relation $L M_\mathrm{PS} \ge 15$. This bound, which is at least a factor of three higher than what observed in QCD, is a likely consequence of the different spectral signatures of the two theories, with the scalar isosinglet ($0^{++}$ glueball) being the lightest particle in our model. In addition to stressing the importance of simulating large lattice sizes, our analysis emphasises the need to understand quantitatively the {\em full} spectrum of the theory rather than just the spectrum in the mesonic isotriplet sector. While for the lightest fermion measuring masses from gluonic operators proves to be still challenging, reliable results for glueball states are obtained at the largest fermion mass and, in the mesonic sector, for both fermion masses. As a byproduct of our investigation, we perform a finite size scaling of the pseudoscalar mass and decay constant. The data presented in this work support the conformal behaviour of this theory with an anomalous dimension $\gamma_* \simeq 0.37$., Comment: 17 pages

We investigate non perturbatively scattering properties of Goldstone Bosons in an SU(2) gauge theory with two Wilson fermions in the fundamental representation. Such a theory can be used to build extensions of the Standard Model that unifies Technicolor and pseudo Goldstone composite Higgs models. The leading order contribution to the scattering amplitude of Goldstone bosons at low energy is given by the scattering lengths. In the context of technicolor extensions of the Standard Model the scattering lengths are constrained by WW scattering measurements. We first describe our setup and in particular the expected chiral symmetry breaking pattern. We then discuss how to compute them on the lattice and give preliminary results using finite size methods., Comment: Conference Proceedings, 7 pages and 4 figures. Talk presented at the 32nd International Symposium on Lattice Field Theory, Columbia University, New York City, NY

We provide a pedagogical introduction to extensions of the Standard Model in which the Higgs is composite. These extensions are known as models of dynamical electroweak symmetry breaking or, in brief, Technicolor. Material covered includes: motivations for Technicolor, the construction of underlying gauge theories leading to minimal models of Technicolor, the comparison with electroweak precision data, the low energy effective theory, the spectrum of the states common to most of the Technicolor models, the decays of the composite particles and the experimental signals at the Large Hadron Collider. The level of the presentation is aimed at readers familiar with the Standard Model but who have little or no prior exposure to Technicolor. Several extensions of the Standard Model featuring a composite Higgs can be reduced to the effective Lagrangian introduced in the text. We establish the relevant experimental benchmarks for Vanilla, Running, Walking, and Custodial Technicolor, and a natural fourth family of leptons, by laying out the framework to discover these models at the Large Hadron Collider., Comment: LaTeX, 102 pages. Version to match the published version

Technicolor theories provide an elegant mechanism for dynamical electroweak symmetry breaking. We will discuss the use of lattice simulations to study the strongly-interacting dynamics of some of the candidate theories, with matter fields in representations other than the fundamental. To be viable candidates for phenomenology, such theories need to be different from a scaled-up version of QCD, which were ruled out by LEP precision measurements, and represent a challenge for modern lattice computations., Comment: 16 pages, 9 figures; to appear in the proceedings of the Tenth Workshop on Non-Perturbative Quantum Chromodynamics, Paris, June 8-12, 2009

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 PRD

We present the status of our analysis on the order of the finite temperature transition in QCD with two flavors of degenerate fermions. Our new simulations on large lattices support the hypothesis of the first order nature of the transition, showing a preliminary two state signal. We will discuss the implications and the next steps in our analysis., Comment: 6 pages, 4 figures. Talk presented at The XXVI International Symposium on Lattice Field Theory, July 14 - 19, 2008 - Williamsburg, Virginia, USA

We calculate correlation functions of the energy-momentum tensor in the vicinity of the deconfinement phase transition of (3+1)-dimensional SU(2) gauge theory and discuss their critical behavior in the vicinity of the second order deconfinement transition. We show that correlation functions of the trace of the energy momentum tensor diverge uniformly at the critical point in proportion to the specific heat singularity. Correlation functions of the pressure, on the other hand, stay finite at the critical point. We discuss the consequences of these findings for the analysis of transport coefficients, in particular the bulk viscosity, in the vicinity of a second order phase transition point., Comment: 24 pages, 6 figures

In QCD with adjoint fermions (aQCD) the deconfining transition takes place at a lower temperature than the chiral transition. We study the two transitions by use of the Polyakov Loop, the monopole order parameter and the chiral condensate. The deconfining transition is first order, the chiral is a crossover. The order parameters for confinement are not affected by the chiral transition. We conclude that the degrees of freedom relevant to confinement are different from those describing chiral symmetry., Comment: 5 pages, 6 figures. Minor corrections, acknowledgments, new references and bigger figures

QCD with fermions in the adjoint representation (aQCD) is a model for which a deconfinement and a chiral phase transition take place at different temperatures. In this work, we present a study of the deconfinement transition in the dual superconductor picture based on the evaluation of an operator which carries magnetic charge. The expectation value of this operator signals monopole condensation and is an order parameter for deconfinement as in the case of fermions in the fundamental representation. We find a sharp first order deconfinement transition. We also study the effects of the chiral transition on the monopole order parameter and find them negligible., Comment: 7 pages. Talk presented at the The XXV International Symposium on Lattice Field Theory, July 30-4 August 2007, Regensburg, Germany

We complete our analysis of Nf=2 QCD based on the lattice staggered fermion formulation. Using a series of Monte Carlo simulations at fixed (amq*Ls^yh) one is able to test the universality class with given critical exponent yh. This strategy has been used to test the O(4) universality class and it has been presented at the previous Lattice conferences. No agreement was found with simulations in the mass range amq=[0.01335,0.15] using lattices with Ls=16 up to 32 and Lt=4. With the same strategy, we now investigate the possibility of a first order transition using a new set of Monte Carlo data corresponding to yh=3 in the same mass and volume range as the one used for O(4). A substantial agreement is observed both in the specific heat scaling and in the scaling of the chiral condensate, while the chiral susceptibilities still presents visible deviation from scaling in the mass range explored., Comment: 5 pages, 6 figures, Presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, Germany

This paper is part of a program of investigation of the chiral transition in Nf=2 QCD, started in Phys.Rev.D72:114510,2005. Progress is reported on the understanding of some possible systematic errors. A direct test of first order scaling is presented., Comment: 7 pages, 6 figures

We investigate the dual superconductivity mechanism in the exceptional group $G_2$. This is a centerless group (no 't Hooft flux vortices are allowed) and we check for the presence of a magnetic monopole condensate in the confined phase by measuring on the lattice a disorder parameter related to the vacuum expectation value of an operator carrying magnetic charge. The behaviour of the disorder parameter is consistent with the dual superconductor picture. A first step of an analysis on the thermodynamical properties of the theory is conducted by mean of this operator., Comment: Talk presented at Lattice 2006 Tucson, 7 pages, 5 figures, to be published in POS(LAT2006)063

Two distinct phase transitions occur at different temperatures in QCD with adjoint fermions (aQCD): deconfinement and chiral symmetry restoration. In this model, quarks do no explicitely break the center Z(3) symmetry and therefore the Polyakov loop is a good order parameter for the deconfinement transition. We study monopole condensation by inspecting the expectation value of an operator which creates a monopole. Such a quantity is expected to be an order parameter for the deconfinement transition as in the case of fundamental fermions., Comment: Lattice 2006 proceedings, 5 pages, 2 figures

A Ginsparg-Wilson based calibration of the topological charge is used to calculate the renormalization constants which appear in the field-theoretical determination of the topological susceptibility on the lattice. A systematic comparison is made with calculations based on cooling. The two methods agree within present statistical errors (3%-4%). We also discuss the independence of the multiplicative renormalization constant Z from the background topological charge used to determine it., Comment: 12 pages, Latex source + 4 ps-figures. Expanded discussion on second systematic error + 1 more figure

The study of QCD with two light dynamical fermions is of fundamental importance to understand the mechanism of color confinement. We present results of a numerical investigation on the order of the chiral phase transition with $N_f = 2$ by use of a novel strategy in finite size scaling analysis. We compare the critical behaviour of the specific heat, of the chiral susceptibility and of the equation of state with the possible critical behaviours. A second order transition in the O(4) and O(2) universality classes are excluded by our data and substantial evidence emerges for a first order transition. Like in most of previous works we have used the standard staggered action with $L_t = 4$: possible scaling violations and the need for further studies are discussed., Comment: 6 pages, 9 figures, to appear in the proceedings of Computational Hadron Physics, Nicosia, 14-17 September 2005

Studying the order of the chiral transition for $N_f=2$ is of fundamental importance to understand the mechanism of color confinement. We present results of a numerical investigation on the order of the transition by use of a novel strategy in finite size scaling analysis. The specific heat and a number of susceptibilities are compared with the possible critical behaviours. A second order transition in the O(4) and O(2) universality classes are excluded. Substantial evidence emerges for a first order transition. Results are in agreement with those found by studying the scaling properties of a disorder parameter related to the dual superconductivity mechanism of color confinement., Comment: 7 pages, 11 figures. Talk given at the International Workshop on Quantum Chromodynamics: QCD@Work 2005, Conversano, Italy, 16-20 June 2005

QCD with N_f=2 is a specially interesting system to investigate the chiral transition. The order of the transition has still not been established. We report the results of an in-depth numerical investigation performed with staggered fermions on lattices with L_t=4 and L_s=12,16,20,24,32 and quark masses am_q ranging from 0.01335 to 0.307036. Using finite-size techniques we compare the scaling behavior of a number of thermodynamical susceptibilities with the expectations of O(4) and O(2) universality classes. Clear disagreement is observed. Indications of a first order transition are found., Comment: 6 pages, 4 figures, PoS style. Talk presented at Lattice 2005 (Nonzero temperature and density), Dublin, Ireland, July 25-30

We present a study of the systematic effects in the nonperturbative evaluation of the renormalization constants which appear in the field-theoretical determination of the topological susceptibility in pure Yang-Mills theory. The study is performed by computing the renormalization constants on configurations that have been calibrated by use of the Ginsparg-Wilson formalism and by cooling., Comment: 6 pages; Talk presented at Lattice 2005 (Topology), Dublin, July 25-30, 2005

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., Comment: 6 pages, 3 eps figures, REVTex4

We argue that the order of the chiral transition for N_f=2 is a sensitive probe of the QCD vacuum, in particular of the mechanism of color confinement. A strategy is developed to investigate the order of the transition by use of finite size scaling analysis. An in-depth numerical investigation is performed with staggered fermions on lattices with N_t=4 and N_s=12,16,20,24,32 and quark masses am_q ranging from 0.01335 to 0.307036. The specific heat and a number of susceptibilities are measured and compared with the expectations of an O(4) second order and of a first order phase transition. A second order transition in the O(4) and O(2) universality classes are excluded. Substantial evidence emerges for a first order transition. A detailed comparison with previous works is performed., Comment: 46 pages, 20 eps figures, 9 tables, REVTeX4

A careful study is made on the lattice of the phase diagram of QCD with two staggered flavors, to investigate the order of the chiral transition of N_f=2 QCD. The specific heat and the susceptibility of the chiral condensate are determined for different spatial sizes of the system, and a finite size scaling analysis provides a determination of the (pseudo)critical indices. The result is a strong indication that the chiral transition is first order., Comment: 6 pages, 11 figures, contribution to the proceedings of the "8th Workshop on Non-Perturbative Quantum Chromodynamics", June 7-11, 2004, Institut Astrophysique de Paris

A strategy is developed to investigate the order of the transition using finite size scaling and its relation to color confinement. An in-depth numerical investigation has been performed with KS fermions on lattices with N_t=4 and N_s=12,16,20,24,32 and quark masses am_q ranging from 0.01335 to 0.35. The specific heat and a number of susceptibilities have been measured and compared with the expectation of an O(4) second order and a first order phase transition. A second order O(4) is excluded, whilst data are consistent with a first order., Comment: 6 pages, 16 postscript figures, based on parallel talks presented at Lattice2004(non-zero), Fermilab, June 21-26, 2004

The transition is studied by means of a disorder parameter detecting condensation of magnetic monopoles in the vacuum. The deconfining transition is found to coincide with the chiral transition and the susceptibility \rho, related to the disorder parameter, is consistent with a first order phase transition., Comment: 3 pages, 2 figures. Poster presented at Lattice2004(topology), Fermilab, June 21-26, 2004

The order and the nature of the finite-temperature phase transition of QCD with two flavors of dynamical quarks is investigated. An analysis of the critical exponent of the specific heat is performed through finite-size and finite-mass scaling of various susceptibilities. Dual superconductivity of QCD vacuum is investigated using a disorder parameter, namely the v.e.v. of a monopole creation operator. Hybrid R simulations were run at lattice spatial sizes of $12^3$, $16^3$, $20^3$ and $32^3$ and temporal size $N_t=4$, with quark masses in the range $am_q = 0.3 - 0.01$., Comment: Lattice2003(topology), 3 pages

We present evidence that in full QCD with two dynamical quarks confinement is produced by dual superconductivity of the vacuum as in the quenched theory. Preliminary information is obtained on the nature of the deconfining transition., Comment: 3 pages, 5 figures, Lattice2002(topology)

We report on evidence from lattice simulations that confinement is produced by dual superconductivity of the vacuum in full QCD as in quenched QCD. Preliminary information is obtained on the order of the deconfining phase transition., Comment: 4 pages, to appear in the Proceedings of Quark Matter 02 - The XVI International Conference on Ultrarelativistic Nucleus-Nucleus Collisions