The knowledge of the phase diagram of strongly coupled theories as function of the number of colors, flavors and matter representation plays a fundamental role when constructing viable extensions of the standard model (SM) featuring dynamical electroweak symmetry breaking. Here I summarize the state-of-the-art of the phase diagram for SU(N) gauge theories with fermionic matter transforming according to arbitrary representations of the underlying gauge group. I critically report on the latest results from first principle lattice simulations and then review the principal models of (near) conformal technicolor such as (Next) Minimal Walking Technicolor (MWT) and Partially Gauged Technicolor (PGT). I finally show that the incarnation of the conformal technicolor model is nothing but the simplest PGT model.
We investigate the structure and the novel emerging features of the mesonic non-singlet spectrum of the Minimal Walking Technicolor (MWT) theory. Precision measurements in the nonsinglet pseudoscalar and vector channels are compared to the expectations for an IR-conformal field theory and a QCD-like theory. Our results favor a scenario in which MWT is (almost) conformal in the infrared, while spontaneous chiral symmetry breaking seems less plausible.
We examine the temperature-dependent electroweak phase transition in extensions of the Standard Model in which the electroweak symmetry is spontaneously broken via strongly coupled, nearly-conformal dynamics. In particular, we focus on the low energy effective theory used to describe Minimal Walking Technicolor at the phase transition. Using the one-loop effective potential with ring improvement, we identify significant regions of parameter space which yield a sufficiently strong first order transition for electroweak baryogenesis. The composite particle spectrum corresponding to these regions…
We construct a complete, realistic, and natural UV completion of minimal conformal technicolor that explains the origin of quark and lepton masses and mixing angles. As in "bosonic technicolor", we embed conformal technicolor in a supersymmetric theory, with supersymmetry broken at a high scale. The exchange of heavy scalar doublets generates higher-dimension interactions between technifermions and quarks and leptons that give rise to quark and lepton masses at the TeV scale. Obtaining a sufficiently large top quark mass requires strong dynamics at the supersymmetry breaking scale in both the …
We investigate the effects of four-fermion interactions on the phase diagram of strongly interacting theories for any representation as function of the number of colors and flavors. We show that the conformal window, for any representation, shrinks with respect to the case in which the four-fermion interactions are neglected. The anomalous dimension of the mass increases beyond the unity value at the lower boundary of the new conformal window. We plot the new phase diagram which can be used, together with the information about the anomalous dimension, to propose ideal models of walking technic…
I discuss recent progress in the uncovering of the phase diagram of non-supersymmetric gauge theories. The nature of the conformal window for higher dimensional representations suggests a possible way to construct realistic technicolor models. I then explicitly provide two such theories. One of these models also has a natural cold Dark Matter candidate.
The recently observed boson at 125 GeV could be a light composite scalar from near-conformal technicolor dynamics: a technicolor Higgs. If this is the case, unitarization of longitudinal weak boson scattering amplitudes, which is due to exchanges of the Higgs and spin-one vector technimesons, is expected to occur in a strong regime, with saturation of the unitarity bounds. This implies that $pp \to V V jj$ processes, where $V$ is either a $W$ or a $Z$ boson, are enhanced, relative to the standard model. We show that this allows probing near-conformal technicolor for couplings and masses of the…
We perform a lattice study of the topological susceptibility and instanton size distribution of the $\su{2}$ gauge theory with two adjoint Dirac fermions (also known as Minimal Walking Technicolor), which is known to be in the conformal window. In the theory deformed with a small mass term, by drawing a comparison with the pure gauge theory, we find that topological observables are decoupled from the fermion dynamics. This provides further evidence for the infrared conformality of the theory. A study of the instanton size distribution shows that this quantity can be used to detect the onset of…
We point out that the flavor problem in theories with dynamical electroweak symmetry breaking can be effectively decoupled if the physics above the TeV scale is strongly conformal, and the electroweak order parameter has a scaling dimension d = 1 + epsilon with epsilon \simeq 1/few. There are many restrictions on small values of epsilon: for epsilon << 1, electroweak symmetry breaking requires a fine-tuning similar to that of the standard model; large-N conformal field theories (including those obtained from the AdS/CFT correspondence) require fine-tuning for d < 2; `walking technicolor' theor…
Conformal technicolor is a paradigm for new physics at LHC that may solve the problems of strong electroweak symmetry breaking for quark masses and precision electroweak data. We give explicit examples of conformal technicolor theories based on a QCD-like sector. We suggest a practical method to test the conformal dynamics of these theories on the lattice.
Slowly walking technicolor models provide a mechanism for electroweak symmetry breaking whose nonperturbative lattice investigation is rather challenging. Here we demonstrate walking near a conformal fixed point considering the 2-d lattice O(3) model at vacuum angle $θ\approx π$. The essential features of walking technicolor models are shared by this toy model and can be accurately investigated by numerical simulations. We show results for the running coupling and the beta-function and we perform a finite size scaling analysis of the massgap close to the conformal point.
The technicolor scenario replaces the Higgs sector of the standard model with a strongly interacting sector. One candidate for a realization of such a sector is two-technicolor Yang-Mills theory coupled to two degenerate flavors of adjoint, massless techniquarks. Using lattice gauge theory the properties of the technigluons in this scenario are investigated as a function of the techniquark mass towards the massless limit. For that purpose the minimal Landau gauge two-point and three-point correlation functions are determined, including a detailed systematic error analysis. The results are, wit…
We study the Yukawa corrections to the gamma gamma --> b\bar{b} corss section in the topcolor assisted technicolor models at the photon-photon colliders. We find that, for the favorable parameters, the relative corrections from pseudo Goldstone bosons give out a 3.2%--5.9% decrement of the cross section from the tree level when \sqrt{s}=500 GeV, the contributions from new extended technicolor gauge bosons Z* and colored gauge bosons B are negligibly small, and the relative correction arising from new color-singlet heavy gauge boson Z' is less than -3.2%. Therefore, the total relative correctio…
We study the minimal model of conformal technicolor, an SU(2) gauge theory near a strongly coupled conformal fixed point, with conformal symmetry softly broken by technifermion mass terms. Conformal symmetry breaking triggers chiral symmetry breaking in the pattern SU(4) -> Sp(4), which gives rise to a pseudo-Nambu-Goldstone boson that can act as a composite Higgs boson. The top quark is elementary, and the top and electroweak gauge loop contributions to the Higgs mass are cut off entirely by Higgs compositeness. In particular, the model requires no top partners and no "little Higgs" mechanism…
In this lecture I give an introduction to technicolor and extended technicolor theories. I discuss the issues models of dynamical electroweak symmetry breaking struggle with and propose how non QCD-like dynamics, such as a `walking' or nearly-conformal technicolor coupling, can invalidate many conventional arguments against technicolor. I provide a short discussion of AdS/CFT-inspired extra-dimensional (Higgsless) models and their similarities and differences with older 4D technicolor models. To conclude, a summary of some possible LHC signatures is given.
Since the pioneering work of Eichten and Lane it has been known that the scale of the interactions responsible for the generation of the strange-quark mass in extended technicolor theories must, absent any "GIM-like" mechanism for suppressing flavor-changing neutral currents, be greater than of order 1000 TeV. In this note we point out that the constraint from the neutral D-meson system is now equally strong, implying that the charm quark mass must also arise from flavor dynamics at a scale this high. We then quantify the degree to which the technicolor condensate must be enhanced in order to …
We explicitly calculate the $S$ parameter in entire parameter space of the holographic walking/conformal technicolor (W/C TC), based on the deformation of the holographic QCD by varying the anomalous dimension from $γ_m \simeq 0$ through $γ_m \simeq 1$ continuously. The $S$ parameter is given as a positive monotonic function of $ξ$ which is fairly insensitive to $γ_m$ and continuously vanishes as $S \sim ξ^2 \to 0$ when $ξ\to 0$, where $ξ$ is the vacuum expectation value of the bulk scalar field at the infrared boundary of the 5th dimension $z=z_m$ and is related to the mass of (techni-) $ρ$ m…
We investigate theories in which the technifermions in higher dimensional representations of the technicolor gauge group dynamically break the electroweak symmetry of the standard model. For the two-index symmetric representation of the gauge group the lowest number of techniflavors needed to render the underlying gauge theory quasi conformal is two. We confront the models with the recent electroweak precision measurements and demonstrate that the two technicolor theory is a valid candidate for a dynamical breaking of the electroweak symmetry. The electroweak precision measurements provide use…
We study the gauge sector of Minimal Walking Technicolor, which is an SU(2) gauge theory with nf=2 flavors of Wilson fermions in the adjoint representation. Numerical simulations are performed on lattices Nt x Ns^3, with Ns ranging from 8 to 16 and Nt=2Ns, at fixed β=2.25, and varying the fermion bare mass m0, so that our numerical results cover the full range of fermion masses from the quenched region to the chiral limit. We present results for the string tension and the glueball spectrum. A comparison of mesonic and gluonic observables leads to the conclusion that the infrared dynamics is gi…
Here I summarize some of the salient features of technicolor theories with technifermions in higher dimensional representations of the technicolor gauge group. The expected phase diagram as function of number of flavors and colors for the two index (anti)symmetric representation of the gauge group is reviewed. After having constructed the simplest walking technicolor theory one can show that it is not at odds with the precision measurements. The simplest theory also requires, for consistency, a fourth family of heavy leptons. The latter may result in an interesting signature at LHC. In the cas…
There are quasi-conformal theories, like the Minimal and Ultraminimal Technicolor models, which may break dynamically the gauge symmetry of the Standard Model and at the same time are compatible with electroweak precision data. The main characteristic of this type of models is their fermionic content in one or more higher dimensional representations, therefore it is not immediate to know which model leads to the most attractive channel or the minimum vacuum energy state. We discuss the effective potential for composite operators for these models, verifying that their vacuum energy values are d…
We unveil the temperature-dependent electroweak phase transition in new extensions of the Standard Model in which the electroweak symmetry is spontaneously broken via strongly coupled, nearly-conformal dynamics achieved by the means of multiple matter representations. In particular, we focus on the low energy effective theory introduced to describe Ultra Minimal Walking Technicolor at the phase transition. Using the one-loop effective potential with ring improvement, we identify regions of parameter space which yield a strong first order transition. A striking feature of the model is the exist…
Dynamical electro-weak symmetry breaking is an appealing, strongly-coupled alternative to the weakly-coupled models based on an elementary scalar field developing a vacuum expectation value. In the first two sections of this set of lectures, I summarize the arguments, based on low-energy phenomenology, supporting walking technicolor as a realistic realization of this idea. This pedagogical introduction to walking technicolor, and more generally to the physics of extensions of the standard model, makes extensive use of effective field theory arguments, symmetries and counting rules. The strongl…
We investigate the physical spectrum of vector-like SU(N) gauge theories with infrared coupling close to but above the critical value for a conformal phase transition. We use dispersion relations, the momentum dependence of the dynamical fermion mass and resonance saturation. We show that the second spectral function sum rule is substantially affected by the continuum contribution, allowing for a reduction of the axial vector - vector mass splitting with respect to QCD-like theories. In technicolor theories, this feature can result in a small or even negative contribution to the electroweak S …
Here we concisely review the nonminimal coupling dynamics of a single scalar field in the context of purely affine gravity and extend the study to multifield dynamics. The coupling is performed via an affine connection and its associated curvature without referring to any metric tensor. The latter arises a posteriori and it may gain an emergent character like the scale of gravity. What is remarkable in affine gravity is the transition from nonminimal to minimal couplings which is realized by only field redefinition of the scalar fields. Consequently, the inflationary models gain a unique descr…
Non-Abelian gauge theories with fermions transforming in the adjoint representation of the gauge group (AdjQCD) are a fundamental ingredient of many models that describe the physics beyond the Standard Model. Two relevant examples are N=1 Supersymmetric Yang-Mills (SYM) theory and Minimal Walking Technicolor, which are gauge theories coupled to one adjoint Majorana and two adjoint Dirac fermions, respectively. While confinement is a property of N=1 SYM, Minimal Walking Technicolor is expected to be infrared conformal. We study the propagators of ghost and gluon fields in the Landau gauge to co…
It is quite possible that the Technicolor problems are related to the poorly known self-energy expression, or the way chiral symmetry breaking (CSB) is realized in non-abelian gauge theories. Actually, the only known laboratory to test the CSB mechanism is QCD. The TC dynamics may be quite different from the QCD , this fact has led to the walking TC proposal making the new strong interaction almost conformal and changing appreciably its dynamical behavior. There are different ways to obtain of extreme walking (or quasi-conformal) technicolor theories, in this paper we propose an scheme to obta…
We propose a new dark matter candidate, {\it light decoupled techni-dilaton}, which arises from the almost scale-invariant/conformal (walking) technicolor. We investigate its characteristic nature and discuss several cosmological and astrophysical constraints. It turns out that techni-dilatons are extremely weakly interacting and produced dominantly by the non-thermal mechanism to be the main component of dark matter with mass range between around 0.01 eV and 500 eV for typical walking technicolor scenarios.
SU(3) gauge theory with dynamical overlap fermions in the 2-index symmetric (sextet) representation is considered. This model may be a viable model of the electroweak symmetry breaking sector along the lines of the walking technicolor paradigm. The number of fermion species is chosen such that the theory is expected to be below the conformal window. We will discuss how the epsilon-regime and random matrix theory can be used to test whether at any given set of parameters (N_c, N_f, representation) the theory is in the conformal phase or indeed just below it. Quenched Monte Carlo results are inc…
We explore the constraining power of OPE associativity in 4D Conformal Field Theory with a continuous global symmetry group. We give a general analysis of crossing symmetry constraints in the 4-point function <Phi Phi Phi* Phi*>, where Phi is a primary scalar operator in a given representation R. These constraints take the form of 'vectorial sum rules' for conformal blocks of operators whose representations appear in R x R and R x Rbar. The coefficients in these sum rules are related to the Fierz transformation matrices for the R x R x Rbar x Rbar invariant tensors. We show that the number of …
We consider the possibility that the new particle that has been observed at 125 GeV is not the Standard Model (SM) Higgs, but instead the dilaton associated with an approximate conformal symmetry that has been spontaneously broken. We focus on dilatons that arise from theories of technicolor, or from theories of the Higgs as a pseudo-Nambu-Goldstone boson (pNGB), that involve strong conformal dynamics in the ultraviolet. In the pNGB case, we are considering a framework where the Higgs particle is significantly heavier than the dilaton and has therefore not yet been observed. In each of the tec…
According to the Ideal Walking Technicolor paradigm large mass anomalous dimensions arise in gauged Nambu--Jona-Lasinio (NJL) models when the four-fermion coupling is sufficiently strong to induce spontaneous symmetry breaking in an otherwise conformal gauge theory. We therefore study the $SU(2)$ gauged NJL model with two adjoint fermions using lattice simulations. The model is in an infrared conformal phase at small NJL coupling while it displays a chirally broken phase at large NJL couplings. In the infrared conformal phase we find that the mass anomalous dimension varies with the NJL coupli…
We examine the effects of standard model-like interactions on the near-conformal dynamics of a theory featuring a dilatonic state identified with the standard model-like Higgs. As template for near-conformal dynamics we use a gauge theory with fermionic matter and elementary mesons possessing the same non-abelian global symmetries as a technicolor-like theory with matter in a complex representation of the gauge group. We then embed the electroweak gauge group within the global flavor structure and add also ordinary quark-like states to mimic the effects of the top. We find that the standard mo…
We consider the possibility of a light composite scalar boson arising from mass mixing between a relatively light and heavy scalar singlets in a see-saw mechanism expected to occur in two-scale Technicolor (TC) models. A light composite scalar boson can be generated when the TC theory features two technifermions species in different representations, $R_1$ and $R_2$, under a single technicolor gauge group, with characteristic scales $Λ_1$ and $Λ_2$. We determine the final composite scalar fields, $Φ_1$ and $Φ_2$, effective theory using the effective potential for composite operators approach. T…
We present new results on chiral symmetry breaking in nearly conformal gauge theories with fermions in the fundamental representation of the SU(3) color gauge group. The number of fermion flavors is varied in an extended range below the conformal window with chiral symmetry breaking ($χ{\rm SB}$) for all flavors between $N_f=4$ and $N_f=12$. To identify $χ{\rm SB}$ we apply several methods which include, within the framework of chiral perturbation theory, the analysis of the Goldstone spectrum in the p-regime and the spectrum of the fermion Dirac operator with eigenvalue distributions of rando…
Based on recent progress in the study of strong dynamics in conformal field theories, I construct a simple, one family model of dynamical electro-weak symmetry breaking. Non-perturbative effects can be computed systematically. The model does not suffer from the well known, parametrically big, phenomenological difficulties of traditional technicolor models, is compatible with all present experimental data and is testable at the LHC.
In contrast to the folklore that Technicolor (TC) is a "Higgsless theory", we shall discuss existence of a composite Higgs boson, Techni-Dilaton (TD), a pseudo-Nambu-Goldstone boson of the scale invariance in the Scale-invariant/Walking/Conformal TC (SWC TC) which generates a large anomalous dimension $γ_m \simeq 1$ in a wide region from the dynamical mass $m$ $= {\cal O}$ (TeV) of the techni-fermion all the way up to the intrinsic scale $Λ_{\rm TC}$ of the SWC TC (analogue of $Λ_{\rm QCD}$), where $Λ_{\rm TC} $ is taken typically as the scale of the Extended TC scale $Λ_{\rm ETC}$: $Λ_{\rm TC…
We investigate the spectrum and IR properties of the SU(3) "sextet" model with two Dirac fermions in the two-index symmetric representation via lattice simulations. This model is a prime candidate for a realization of Walking Technicolor, which features a minimal matter content and it is expected to be inside or very close to the lower boundary of the conformal window. We use the Wilson discretization for the fermions and map the phase structure of the lattice model. We study several spectral and gradient flow observables both in the bulk and the weak coupling phases. While in the bulk phase w…
SU(2) gauge theory with two fermions transforming under the adjoint representation may appear conformal or almost conformal in the infrared, and is one of the candidate theories for building models for technicolor. Early lattice Monte Carlo studies of this model have used unimproved Wilson fermion formulation, which can be expected to have large lattice cutoff effects. In this paper we present the calculation of the O(a) improved lattice Wilson-clover action of the theory. The Sheikholeslami-Wohlert coefficient has been determined non-perturbatively, and various boundary improvement terms, nee…
We introduce the topic of dynamical breaking of the electroweak symmetry and its link to unparticle physics and cosmology. The knowledge of the phase diagram of strongly coupled theories plays a fundamental role when trying to construct viable extensions of the standard model (SM). Therefore we present the state-of-the-art of the phase diagram for SU, Sp and SO gauge theories with fermionic matter transforming according to arbitrary representations of the underlying gauge group. We summarize several analytic methods used recently to acquire information about these gauge theories. We also provi…
We introduce a new numerical algorithm based on semidefinite programming to efficiently compute bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N=1 superconformal field theories. Using our algorithm, we dramatically improve previous bounds on a number of CFT quantities, particularly for theories with global symmetries. In the case of SO(4) or SU(2) symmetry, our bounds severely constrain models of conformal technicolor. In N=1 superconformal theories, we place strong bounds on dim(Phi*Phi), where Phi is a chiral operator. These bounds asymptote to the l…
Scalar composite boson masses have been computed in QCD and Technicolor theories with the help of the homogeneous Bethe-Salpeter equation (BSE), resulting in a scalar mass that is twice the dynamically generated fermion or technifermion mass ($m_{dyn}$). We show that in the case of walking (or quasi-conformal) technicolor theories, where the $m_{dyn}$ behavior with the momenta may be quite different from the one predicted by the standard operator product expansion, this result is incomplete and we must consider the effect of the normalization condition of the BSE to determine the scalar masses…
A genuine dilaton $σ$ allows scales to exist even in the limit of exact conformal invariance. In gauge theories, these may occur at an infrared fixed point (IRFP) $α_{\text{IR}}$ through dimensional transmutation. These large scales at $α_{\text{IR}}$ can be separated from small scales produced by $θ^μ_μ$, the trace of the energy-momentum tensor. For quantum chromodynamics (QCD), the conformal limit can be combined with chiral $SU(3) \times SU(3)$ symmetry to produce chiral-scale perturbation theory $χ$PT$_σ$, with $f_0(500)$ as the dilaton. The technicolor (TC) analogue of this is crawling TC…
We propose an approach for the calculation of the yukawa coupling through the scalar decay constant and the chiral condensate in the context of the extended technicolor (ETC). We perform the nonperturbative computation of the yukawa coupling based on the improved ladder Schwinger-Dyson equation. It turns out that the yukawa coupling can be larger or smaller than the standard model (SM) value, depending on the number $N_D$ of the weak doublets for each technicolor (TC) index. It is thus nontrivial whether or not the huge enhancement of the production of the scalar via the gluon fusion takes pla…
We show that it is possible to construct explicit models of electroweak symmetry breaking in which the number of techniflavors needed to enter the conformal phase of the theory is small and weakly dependent on the number of technicolors. Surprisingly, the minimal model with {\it just} two (techni)flavors, together with a suitable gauge dynamics, can be made almost conformal. The theories we consider are generalizations of orientifold type gauge theories, in which the fermions are in either two index symmetric or antisymmetric representation of the gauge group, as the underlying dynamics respon…
We introduce fundamental gauge theories that can be employed to construct informed composite bright and dark extensions of the Standard Model, within and beyond the standard paradigms. The gap between theory and experiments is bridged by providing predictions and ways to test them, for example, at the Fermi scale and via precision flavor experiments. We will review time-honoured paradigms from (walking) technicolor to composite Goldstone Higgs and discuss their features and differences. Standard model fermion mass generation in composite models will also be discussed along with the challenges …
