The phase diagrams at high temperature of SU(N) gauge theories with massive fermions are calculated by numerically minimizing the one-loop effective potential. We consider fermions in the Fundamental (F), Adjoint (Adj), Antisymmetric (AS), and Symmetric (S) representations, for N from 3 to 9, with periodic and antiperiodic boundary conditions applied. For one flavour of AS/S (Dirac) fermion with periodic boundary conditions the C-breaking phase is favoured perturbatively for all values of the fermion mass. In the case of one flavour of adjoint Majorana fermion, and periodic boundary conditons, the deconfined phase is favoured for any fermion mass. For one or more adjoint Dirac fermion (two or more Majorana fermions) we find partially-confining phases as well as new phases with unusual properties. Our results for SU(3) and SU(4) are consistent with our lattice simulations of a related model.
We calculate the phase diagrams at high temperature of SU(N) gauge theories with massive fermions by minimizing the one-loop effective potential. Considering fermions in the adjoint (Adj) representation at various N we observe a variety of phases when Nf >= 2 Majorana flavours and periodic boundary conditions are applied to fermions. Also the confined phase is perturbatively accessible. For N = 3, we add Fundamental (F) representation fermions with antiperiodic boundary conditions to adjoint QCD to show how the Z(3)-symmetry breaks in the confined phase.
We investigate the mass of the $1^{-+}$ exotic meson, created with hybrid interpolating fields. Access to light quark masses approaching 25 MeV is facilitated by the use of the Fat-Link Irrelevant Clover (FLIC) fermion action, and large ($20^3 \times 40$) lattices. Our results indicate that the $1^{-+}$ exotic exhibits significant curvature close to the chiral limit, and yield a $1^{-+}$ mass in agreement with the $π_1 (1600)$ candidate and exclusive of the $π_1 (1400)$.
We study two flavors of massless staggered fermions interacting via an on-site four-fermion inter- action and argue that the model contains an exotic quantum critical point separating the perturba- tive massless phase from a massive fermion phase at strong couplings where the fermion bilinear condensate remains zero. We believe that no spontaneous symmetry breaking occurs at the tran- sition. We have extensive calculations in three Euclidian dimensions that are consistent with the existence of a single second order phase transition separating the two phases. Although mean field theory suggests…
We summarize our measurement of the mass of the exotic $1^{-+}$ hybrid meson using an improved Kogut-Susskind action. We show results from both quenched and dynamical quark simulations and compare with results from Wilson quarks. Extrapolation of these results to the physical quark mass allows comparison with experimental candidates for the $1^{-+}$ hybrid meson.
We investigate the phase structure of a four dimensional SO(4) invariant lattice Higgs-Yukawa model comprising four reduced staggered fermions interacting with a real scalar field. The fermions belong to the fundamental representation of the symmetry group while the three scalar field components transform in the self-dual representation of SO(4). We explore the phase diagram and find evidence of a continuous transition between a phase where the fermions are massless to one where the fermions acquire mass. This transition is not associated with symmetry breaking and there is no obvious local or…
The spectral properties of hybrid meson interpolating fields are investigated. The quantum numbers of the meson are carried by smeared-source fermion operators and highly-improved chromo-electric and -magnetic field operators composed with APE-smeared links. The effective masses of standard and hybrid operators indicate that the ground state meson is effectively isolated using both standard and hybrid interpolating fields. Focus is placed on interpolating fields in which the large spinor components of the quark and antiquark fields are merged. In particular, the effective mass of the exotic $1…
We propose to induce QCD by fermions in the adjoint representation of the gauge group SU(N_c) on the lattice. We consider various types of lattice fermions: chiral, Kogut--Susskind and Wilson ones. Using the mean field method we show that a first order large-N phase transition occurs with decreasing fermion mass. We conclude, therefore, that adjoint fermions induce QCD. We draw the same conclusion for the adjoint scalar or fermion models at large number of flavors N_f when they induce a single-plaquette lattice gauge theory. We find an exact strong coupling solution for the adjoint fermion mod…
We study a lattice field theory model containing two flavors of massless staggered fermions with an onsite four-fermion interaction. The model contains a $SU(4)$ symmetry which forbids non-zero fermion bilinear mass terms, due to which there is a massless fermion phase at weak couplings. However, even at strong couplings fermion bilinear condensates do not appear in our model, although fermions do become massive. While the existence of this exotic strongly coupled massive fermion phase was established long ago, the nature of the transition between the massless and the massive phase has remaine…
Large N gauge theories with adjoint matter can be numerically studied using lattice techniques. Eguchi-Kawai reductions holds for this theory and one can reduce the lattice model to a single site. Hybrid Monte Carlo algorithm can be used to simulate this model. One can either perform an exact computation of the "fermionic force" or use pseudo fermions as part of the HMC algorithm. The former algorithm is slower than the latter but has the advantage that one can work with any real number for the fermion flavor. Some results using both algorithms will be presented.
We consider the large N limit of four dimensional SU(N) Yang-Mills field coupled to adjoint fermions on a single site lattice. We use perturbative techniques to show that the Z^4_N center-symmetries are broken with naive fermions but they are not broken with overlap fermions. We use numerical techniques to support this result. Furthermore, we present evidence for a non-zero chiral condensate for one and two Majorana flavors at one value of the lattice gauge coupling.
We consider the leading-order expression at weak-coupling for a single-site large-N gauge theory coupled to adjoint fermions. We study the case of overlap and wilson fermions. We extend the theory to real values of the number of fermion flavors and restrict ourselves to asymptotically free theories. Using a four-dimensional density function for the distribution of the eigenvalues of the link variables, we show that it is possible to recover the infinite-volume continuum limit for a certain range of fermion flavors if we use fermions with a bare mass of zero. Our use of the four-dimensional den…
The twisted space-time reduced model of large $N$ QCD with various flavours of adjoint Wilson fermions is constructed applying the symmetric twist boundary conditions with flux $k$. The models with one and two flavours show distinctive behaviours. For the two flavor case, the string tension, calculated at $N=289$, approaches zero as we decrease the quark mass in a way consistent with the theory being governed by an infrared fixed point. In contrast, the string tension for the case of a single adjoint Wilson fermion remains finite as the quark mass decreases to zero, supporting that this is a c…
We analyze the large $N$ limit of adjoint QCD, an $SU(N)$ gauge theory with $N_f$ flavors of massless adjoint Majorana fermions, compactified on $S^3 \times S^1$. We focus on the weakly-coupled confining small-$S^3$ regime. If the fermions are given periodic boundary conditions on $S^1$, we show that there are large cancellations between bosonic and fermionic contributions to the twisted partition function. These cancellations follow a pattern previously seen in the context of misaligned supersymmetry, and lead to the absence of Hagedorn instabilities for any $S^1$ size $L$, even though the bo…
We analyze the theory of softly broken supersymmetric $QCD$. Exotic behavior like spontaneously broken baryon number, massless composite fermions and Seiberg's duality seems to persist also in the presence of (small) soft supersymmetry breaking. We argue that certain, specially tailored, lattice simulations may be able to detect the novel phenomena. Most of the exotic behavior does not survive the decoupling limit of large SUSY breaking parameters.
We study four dimensional large-N SU(N) Yang-Mills theory coupled to adjoint overlap fermions on a single site lattice. Lattice simulations along with perturbation theory show that the bare quark mass has to be taken to zero as one takes the continuum limit in order to be in the physically relevant center-symmetric phase. But, it seems that it is possible to take the continuum limit with any renormalized quark mass and still be in the center-symmetric physics. We have also conducted a study of the correlations between Polyakov loop operators in different directions and obtained the range for t…
We construct the magnetic dual of QCD with one adjoint Weyl fermion. The dual is a consistent solution of the 't Hooft anomaly matching conditions, allows for flavor decoupling and remarkably constitutes the first nonsupersymmetric dual valid for any number of colors. The dual allows to bound the anomalous dimension of the Dirac fermion mass operator to be less than one in the conformal window.
It is believed that fermions in adjoint representation on single site lattice will restore the center symmetry, which is a crucial requirement for the volume independence of large-N lattice gauge theories. We present a perturbative analysis which supports the assumption for overlap fermions, but shows that center symmetry is broken for naive fermions.
We analyze the finite temperature phase diagram of QCD with fermions in the adjoint representation. The simulations performed with four dynamical Majorana fermions, which is equivalent to two Dirac fermions, show that the deconfinement and chiral phase transitions occur at two distinct temperatures, $T_{\rm chiral} \simeq 6.65 T_{\rm deconf}$. While the deconfinement transition is first order we find evidence for a continuous chiral transition. We also present potentials for $T<T_{\rm deconf}$ and $T_{\rm deconf}<T< T_{\rm chiral}$ both for fundamental and adjoint fermion-antifermion pairs.
The static potentials for quark-antiquark-gluon and 3-gluon systems are computed with lattice QCD methods. For the quark-antiquark-gluon hybrid meson the static potential is obtained for different values of the angle between the quark-gluon and antiquark-gluon segments. The simulations support the formation of an adjoint string for small angles, while for large angles, the adjoint string is replaced by two fundamental strings connecting the gluon and the quarks. For the 3-gluon glueball, we discuss the corresponding Wilson loops and show that the gluons are connected by fundamental strings whe…
We present a perturbative calculation of the improvement coefficients of SU(2) gauge theory with adjoint representation Wilson-clover fermions and using Schrodinger functional boundary conditions. The computation of the boundary improvement terms is necessary for the full O(a) improvement. With two flavours of adjoint representation fermions this theory is called Minimal Walking Technicolor model.
The QCD-like gauge theory with adjoint fermions is considered in the field correlator formalism and the total spectrum of mesons and glueballs is obtained in agreement with available lattice data. A new state of a white fermion appears, as a bound state of the adjoint fermion and gluon with the mass close to that of glueball. It is shown, that the main features of spectra and thermodynamics of adjoint fermions can be explained by this new bound state.
We consider a single site large N gauge theory coupled to adjoint fermions at weak coupling. We study the distribution of the eigenvalues of the link variables using a four-dimensional density function. We show that it is possible to recover the infinite-volume continuum limit for a certain range of fermion flavors if we use fermions with a bare mass of zero.
Expansions of the Wilson determinant in lattice QCD with quarks produce gauge action terms which shift the coupling constant of the fundamental representation plaquette action and induce an adjoint representation plaquette action. We study the magnitude of these induced couplings with two flavors of Wilson fermions. We utilize a microcanonical demon method, which allows us to measure the induced couplings directly from gauge configurations generated by full fermionic simulations.
Four fermion interactions appear in many models of Beyond Standard Model physics. In Technicolour and composite Higgs models Standard Model fermion masses can be generated by four fermion terms. They are also expected to modify the dynamics of the new strongly interacting sector. In particular in technicolour models it has been suggested that they can be used to break infrared conformality and produce a walking theory with a large mass anomalous dimension. We study the SU(2) gauge theory with 2 adjoint fermions and a chirally symmetric four fermion term. We demonstrate chiral symmetry breaking…
We present a measurement of the Schrödinger Functional running coupling in SU(2) lattice gauge theory with adjoint fermions. We use HEX smearing and clover improvement to reduce the discretization effects. We obtain a robust continuum limit for the step scaling, which confirms the existence of a non-trivial fixed point.
The research of strongly coupled beyond-the-standard-model theories has generated significant interest in non-abelian gauge field theories with different number of fermions in different representations. Motivated by the increased interest to various technicolor scenarios, we study the non-perturbative improvement of the Wilson-clover action with SU(2) gauge fields and 2 flavors of fermions in the fundamental and adjoint representations. The Sheikholeslami-Wohlert coefficients are fixed using Schroedinger functional boundary conditions. The adjoint representation theory is a candidate for a "mi…
The infrared effective theory of adjoint QCD with one Dirac flavour is still under debate. The theory could be confining, conformal, or with a massless fermion in the infrared. The study of chiral symmetry seems to be important to answer this question. While previous investigations have considered Wilson fermions, we present here the first results for this theory based on overlap fermions to avoid explicit chiral symmetry breaking. These indicate spontaneous chiral symmetry breaking by the formation of a fermion condensate. We have also investigated the running coupling of the theory, which in…
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 lim…
Taming finite-volume effects is a crucial ingredient in order to identify the existence of IR fixed points. We present the latest results from our numerical simulations of SU(2) gauge theory with 2 Dirac fermions in the adjoint representation on large volumes. We compare with previous results, and extrapolate to thermodynamic limit when possible.
Clover improvement is the standard choice for lattice simulations of QCD, when the lattice artefacts coming from Wilson fermions have to be reduced. However, the clover improvement is not limited to QCD, but can be applied to a wider range of theories with fermions in higher representations of the gauge group SU(N), like the adjoint fermions required by supersymmetry or by technicolor theories. We present the calculation of the clover coefficient up to one loop order with standard perturbation theory for these models. Applications of clover fermions to supersymmetric Yang-Mills theory are also…
We analyze the large-N behavior of SU(N) lattice gauge theories with adjoint fermions by studying volume-reduced models, as pioneered by Eguchi and Kawai. We perform simulations on a single-site lattice for Nf = 1 and Nf = 2 Wilson Dirac fermions with values of N up to 53. We show for both values of Nf that in the large-N limit there is a finite region, containing both light and heavy fermions, of unbroken center symmetry where the theory exhibits volume independence. Using large-N reduction we attempt to calculate physical quantities such as the string tension and meson masses.
We measure the evolution of the coupling constant using the Schroedinger functional method in the lattice formulation of SU(2) gauge theory with two massless Dirac fermions in the adjoint representation. We observe strong evidence for an infrared fixed point, where the theory becomes conformal. We measure the continuum beta-function and the coupling constant as a function of the energy scale.
We analyze the finite temperature phase diagram of$QC$ with fermions in the adjoint representation. The simulations performed with four dynamical Majorana fermions show that the deconfinement and chiral phase transitions occur at two distinct temperatures. While the deconfinement transition is first order at T_d we find evidence for a continuous chiral transition at a higher temperature $T_c ~ 8 T_d. We observe a rapid change of bulk thermodynamic observables at T_d which reflects the increase in the number of degrees of freedom. However, these show little variation at T_c, where the fermion c…
Recent work on QCD-like theories has shown that the addition of adjoint fermions obeying periodic boundary conditions to gauge theories on $R^{3}\times S^{1}$ can lead to a restoration of center symmetry and confinement for sufficiently small circumference $L$ of $S^{1}$. At small $L$, perturbation theory may be used reliably to compute the effective potential for the Polyakov loop $P$ in the compact direction. Periodic adjoint fermions act in opposition to the gauge fields, which by themselves would lead to a deconfined phase at small $L$. In order for the fermionic effects to dominate gauge …
We derive analytic formulas for the zero-modes of the Dirac equation in the adjoint representation in the background field of Q=1 SU(N) calorons. Solutions with various boundary conditions are obtained, including the physically most relevant cases of periodic and antiperiodic ones. The latter are essential ingredients in a semiclassical treatment of finite temperature supersymmetric Yang-Mills theory. A detailed discussion of adjoint zero-modes in several other contexts is also presented.
We present preliminary results of lattice simulations of SU(2) gauge theory with two Wilson fermions in the adjoint representation. This theory has recently attracted considerable attention because it might possess an infrared fixed point (or an almost-fixed-point), and hence be a candidate for a walking technicolor theory. In this work we study the particle spectrum of the theory, and compare it with more familiar spectrum of the theory with SU(2) gauge fields and two flavors of fundamental representation fermions.
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…
We investigate differences and similarities between fundamental fermions and adjoint fermions in SU(N) gauge theories. The gauge theory with fundamental fermions possesses ZN symmetry only in the limit of infinite fermion mass, whereas the gauge theory with adjoint fermions does have the symmetry for any fermion mass. The flavor-dependent twisted boundary condition (FTBC) is then imposed on fundamental fermions so that the theory with fundamental fermions can possess ZN symmetry for any fermion mass. We show similarities between FTBC fundamental fermions and adjoint fermions, using the Polyako…
The twisted reduced model of large $N$ QCD with two adjoint Wilson fermions is studied numerically using the Hybrid Monte Carlo method. This is the one-site model, whose large $N$ limit (large volume limit) is expected to be conformal or nearly conformal. The string tension calculated at $N$=289 approaches zero as we decrease quark mass and the preliminary value of the mass anomalous dimension $γ_*$ is close to one if we assume that the theory is governed by an infrared fixed point. We also discuss the twisted reduced model with single adjoint Wilson fermion. The string tension remains finite …
We present some results for SU(2) with one adjoint Dirac flavour from lattice studies. Data for the spectroscopy, the static potential, topological charge, and the anomalous dimension of the fermionic condensate are included. Our findings are found to be in- consistent with conventional confining behaviour, instead pointing tentatively towards a theory lying within or very near the onset of the conformal window, with an anomalous dimension of the fermionic condensate of almost 1. Implications of these findings on the building of models of strongly-interacting dynamics beyond the standard model…
We study SU(2) gauge theory with two fermion flavors in the adjoint representation. Using a clover improved HEX smeared action and the gradient flow running coupling allows us to simulate with larger lattice size than before. We find an infrared fixed point after a continuum extrapolation in the range $4.5 \lesssim g^{*2} \lesssim 5$. We also measure the mass anomalous dimension and find the value $ 0.25 \lesssim γ^* \lesssim 0.28 $ at the fixed point.
In this work we investigate the infrared behaviour of a Yang-Mills theory coupled to a massless fermion in the adjoint representation of the gauge group SU(2). This model has many interesting properties, corresponding to the $\mathcal{N}=2$ Super-Yang-Mills theory without scalars and in the recent years there has been an increasing interest toward understanding whether confinement and fermion condensation occur at low energy. We simulate the theory on the lattice close to the massless limit using the overlap discretization of the fermion action, allowing a precise and clean study of the chiral…
To investigate the properties of the large $N$ limit of $\mathcal{N} = 1$ SUSY Yang-Mills theory, we have started a study for a reduced matrix model with an adjoint Majorana fermion. The gauge action is based on the Wilson action and the adjoint-fermion one is the Wilson-Dirac action on a reduced lattice with twisted gauge boundary condition. We employ the RHMC algorithm in which the absolute value of the Pfaffian is incorporated. The sign of the Pfaffian is included with the re-weighting method and separately measured as an observable. In this talk, we show the configuration generation status…
Theories with fermions in the adjoint representation have several interesting applications in extensions of the standard model. The conformal window for these theories is of particular interest for technicolour extensions. We present here our newest results for the spectrum of $N_f=2$ adjoint QCD and compare them with the predictions for a conformal behaviour. The comparison with supersymmetric Yang-Mills theory, investigated with the same methods, will help to distinguish more clearly the conformal and the confining scenario. The spectrum includes additional fermionic states that are not pres…
{We present the results of a numerical investigation of SU(2) gauge theory with $N_f=3/2$ flavours of fermions, corresponding to 3 Majorana fermions, which transform in the adjoint representation of the gauge group. At two values of the gauge coupling, the masses of bound states are considered as a function of the PCAC quark mass. The scaling of bound states masses indicates an infrared conformal behaviour of the theory. We obtain estimates for the fixed-point value of the mass anomalous dimension $γ^*$ from the scaling of masses and from the scaling of the mode number of the Wilson-Dirac oper…
It has been proposed that four-dimensional QCD with fermions in the adjoint representation exhibits volume-independence in the large-N limit. If correct, this would mean that results for physical quantities could be obtained from the single-site version of the model. A necessary condition for volume-independence is that the (Z_N)^4 center-symmetry of the single-site theory is unbroken. We explore the phase diagram of the theory with a single Dirac fermion using Wilson fermions for a number of colors in the range N=8-15, and identify the region in the parameter space of quark mass and gauge cou…
We present a first exploratory study of SU(2) gauge theory with one Dirac flavour in the adjoint representation. We provide initial results for the spectroscopy and the anomalous dimension for the chiral condensate. Our investigation indicates that the theory is conformal or near-conformal, with an anomalous dimension of order one. A discussion of the relevance of these findings in relation to walking technicolor scenarios is also presented.
We study quenched SU(2) lattice gauge theory with adjoint fermions in a wide range of temperatures. We focus on spectral quantities of the Dirac operator and use the temporal fermionic boundary conditions as a tool to probe the system. We determine the deconfinement temperature through the Polyakov loop, and the chiral symmetry restoration temperature for adjoint fermions through the gap in the Dirac spectrum. This chiral transition temperature is about four times larger than the deconfinement temperature. In between the two transitions we find that the system is characterized by a non-vanishi…
We simulate SU(2) gauge theory with two massless Dirac fermions in the adjoint representation. We calculate the running of the Schroedinger Functional coupling and the renormalised quark mass over a wide range of length scales. The running of the coupling is consistent with the existence of an infrared fixed point (IRFP), and we find 0.07 < gamma < 0.56 at the IRFP, depending on the value of the critical coupling.
We apply Schrodinger-functional techniques to the SU(2) lattice gauge theory with N_f=2 flavors of fermions in the adjoint representation. Our use of hypercubic smearing enables us to work at stronger couplings than did previous studies, before encountering a critical point and a bulk phase boundary. Measurement of the running coupling constant gives evidence of an infrared fixed point g* where 1/g*^2 = 0.20(4)(3). At the fixed point, we find a mass anomalous dimension gamma_m(g*) = 0.31(6).
