Monte Carlo simulation of SU(2) gauge theory with fermions on a four-dimensional lattice

After integration over the fermions in an SU(2) lattice gauge theory, the effective fermionic action may be expressed as a sum over all possible closed gauge field loops with corresponding weight factors. We approximate this sum and perform a Monte Carlo simulation of a coupled fermion-gauge system on a 4⁴ lattice. We compare our results for 〈S_eff〉 and $\text{〈}\text{ψ}\text{ψ〉}$ for different values of the gauge field coupling β and fermion coupling κ with the free fermion theory on a lattice. 〈S_eff〉 turns out to be quite small for $\text{κ?}\text{1}\text{8}$.     

A Wilson-Yukawa Model with undoubled chiral fermions in 2D

We consider the fermion mass spectrum in the strong coupling vortex phase (VXS) of a lattice fermion-scalar model with a global U(1)_L × U(1)_R, in two dimensions, in the context of a recently proposed two-cutoff lattice formulation. The fermion doublers are made massive by a strong Wilson-Yukawa coupling, but in contrast with the standard formulation of these type of models, in which the light fermion spectrum was found to be vector-like, we find massless fermions with chiral quantum numbers at finite lattice spacing. When the global symmetry is gauged, this model is expected to give rise to a lattice chiral gauge theory.     

Axial-vector anomaly for Dirac-Kähler fermions on the lattice

The axial-vector current of Dirac-Kähler fermions on the lattice is studied. We consider a U(1) gauge theory in two dimensions as well as an SU(N) gauge theory in four dimensions. Using a short-distance expansion of the fermion propagator in an external gauge field, we show that the correct anomaly is reproduced in the continuum limit.     

Gauge group breaking by Wilson loops

We examine the breaking of gauge symmetries by Wilson loops in the Hosotani-Toms model by determining the background gauge field which minimises the one-loop effective potential for massless Dirac fermions. For anti-periodic fermions, all gauge groups remain unbroken. For periodic fermions, the groups G₂, F₄ and E₈ are broken by quantum corrections due to fermions in any irreducible representation, whereas E₆, E₇ and the classical groups only break if the fermion representation is in the same congruency class as the adjoint.     

Nearly conformal gauge theories in finite volume

We report new results on nearly conformal gauge theories with fermions in the fundamental representation of the SU(3)$\mathit{SU}(3)$ color gauge group as the number of fermion flavors is varied in the Nf=4–16$N_f=4\text{–}16$ range. To unambiguously identify the chirally broken phase below the conformal window we apply a comprehensive lattice tool set in finite volumes which includes the test of Goldstone pion dynamics, the spectrum of the fermion Dirac operator, and eigenvalue distributions of random matrix theory. We also discuss the theory inside the conformal window and present our first results on the running of the renormalized gauge coupling and the renormalization group beta function. The importance of understanding finite volume zero momentum gauge field dynamics inside the conformal window is illustrated. Staggered lattice fermions are used throughout the calculations.     

On the theory of interacting fields in the Foldy-Wouthuysen representation

The overview is devoted to quantum electrodynamics (QED) and the Standard Model in the Foldy-Wouthuysen representation. The Hamiltonian H _FW in the form of a power series in charge e is obtained as applied to the electromagnetic interaction in the FW representation. Quantum electrodynamics in lowest-order perturbation theory is examined. Calculations of specific QED processes are presented. For external fermion lines (p _f ² = m ²), a possibility to expand the scattering matrix, in powers of the coupling constant with matrix elements, not including fermion propagators, is shown. To take into account particle-antiparticle interaction, a modification of the Foldy-Wouthuysen representation is proposed. Fermions in the modified FW representation can be in two states that are characterized by the sign of a third component of the isotopic spin T _f ³ . The sign of T _f ³ is connected with the sign at mass terms in the modified Hamiltonian H _FW. Real fermions (p _f ² = m _f ² ), as well as antifermions, can interact with each other, while real fermions with a given sign of T _f ³ can only interact with real antifermions with the opposite sign of T _f ³ , and vice versa. The formulation of the Standard Model in the FW representation does not necessarily require an interaction of Higgs bosons with fermions. In this approach, the role of Higgs bosons narrows considerably as they are responsible only for gauge invariance of the theory and interact only with gauge bosons. Quantum electrodynamics in the FW representation is invariant under C, P, and T transformations. Weak interaction does not conserve C and P parity, but conserves combined CP parity. The theory allows a connection of CP violation and total or partial violation of isotopic symmetry in the modified Foldy-Wouthuysen representation.     

Spectrum of lattice gauge theories with fermions from a 1/d expansion at strong coupling

We study the strong coupling limit of U(N) or SU(N) gauge theories with fermions on a lattice. The integration over the gauge and fermion degrees of freedom is performed by analytic methods, leading to a partition function in terms of localized meson and baryon fields. A method for deriving a systematic expansion in the inverse of the space-time dimension of the corresponding Green functions is developed. It is applied to the study of spontaneous breakdown of chiral symmetry, which occurs for any U(N) or SU(N) theory with fermions in the fundamental representation. Meson and baryon spectra are then computed, and found to be in close agreement with those obtained by numerical methods at finite coupling. The pion decay constant is estimated.     

Structural Aspects of the Fermion-Boson Mapping in Two-Dimensional Gauge and Anomalous Gauge Theories with Massive Fermions

Using a synthesis of the functional integral and operator approaches we discuss the fermion-boson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In QED₂ with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In anomalous chiral QED₂ with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of Θ-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess-Zumino field replicates the theory, changing neither its algebraic content nor its physical content.     

Phases of renormalized lattice gauge theories with fermions

Starting from the formulation of gauge theories on a lattice we derive renormalization group transformation of the Migdal-Kadanoff type in the presence of fermions. We consider the effect of the fermion vacuum polarization on the gauge Lagrangian but we neglect fermion mass renormalization. We work out the weak coupling and strong coupling expansion in the same framework. Asymptotic freedom is recovered for the non-Abelian case provided the number of fermion multiplets is lower than a critical number. Fixed points are determined both for the U(1) and SU(2) case. We determine the renormalized trajectories and the phases of the theory.     

Adjoint QCD1 + 1 in light-cone gauge, quantized at equal time

SU (2) gauge theory coupled to massless fermions in the adjoint representation is quantized in light-cone gauge by imposing the equal-time canonical algebra. The theory is defined on a space-time cylinder with “twisted” boundary conditions, periodic for one color component (the diagonal 3-component) and antiperiodic for the other two. The focus of the study is on the non-trivial vacuum structure and the fermion condensate. It is shown that the indefinite-metric quantization of free gauge bosons is not compatible with the residual gauge symmetry of the interacting theory. A suitable quantization of the unphysical modes of the gauge field is necessary in order to guarantee the consistency of the subsidiary condition and allow the quantum representation of the residual gauge symmetry of the classical Lagrangian: the 3-color component of the gauge field must be quantized in a space with an indefinite metric while the other two components require a positive-definite metric. The contribution of the latter to the free Hamiltonian becomes highly pathological in this representation, but a larger portion of the interacting Hamiltonian can be diagonalized, thus allowing perturbative calculations to be performed. The vacuum is evaluated through second order in perturbation theory and this result is used for an approximate determination of the fermion condensate.     

Hadron masses in QCD with one quark flavour

One-flavour QCD – a gauge theory with SU(3) colour gauge group and a fermion in the fundamental representation – is studied by Monte Carlo simulations. The mass spectrum of the hadronic bound states is investigated in a volume with extensions of L≃4.4r₀ (≃ 2.2 fm) at two different lattice spacings: a≃0.37r₀ (≃ 0.19 fm) and a≃0.27r₀ (≃ 0.13 fm). The lattice action is a Symanzik tree-level improved Wilson action for the gauge field and an (unimproved) Wilson action for the fermion.     

The relation between the waveguide and overlap implementations of Kaplan's domain wall fermions

Recently, Narayanan and Neuberger proposed that the fermion determinant for a lattice chiral gauge theory be defined by an overlap formula. The motivation for that formula comes from Kaplan's five-dimensional lattice domain wall fermions. In the case that the target continuum theory contains 4n chiral families, we show that the effective action defined by overlap formula is identical to the effective action of a modified waveguide model that has extra bosonic ghost fields. This raises serious questions about the viability of the overlap formula for defining chiral gauge theories on the lattice.     

Composite hadrons in non-Abelian lattice gauge theories

Euclidean non-Abelian gauge theories are quantized on a (finite) lattice using functional integration. From the general from of the 2m-point Schwinger function for the fundamental fermions fields, dynamical consequences for composite meson and fermion fields are investigated. The Okubo-Zweig-Iizuka rule is derived and an analogy to non-relativistic potentials for the quark-antiquark and the 3-quark system is exhibited.     

Twelve massless flavors and three colors below the conformal window

We report new results for a frequently discussed gauge theory with twelve fermion flavors in the fundamental representation of the SU(3) color gauge group. The model, controversial with respect to its conformality, is important in non-perturbative studies searching for a viable composite Higgs mechanism beyond the Standard Model (BSM). In comparison with earlier work, our new simulations apply larger volumes and probe deeper in fermion and pion masses toward the chiral limit. Investigating the controversy, we subject the model to opposite hypotheses with respect to the conformal window. In the first hypothesis, below the conformal window, we test chiral symmetry breaking (χSB) with its Goldstone spectrum, Fπ, the χSB condensate, and several composite hadron states as analytic functions of the fermion mass when varied in a limited range with our best effort to control finite volume effects. In the second test, for the alternate hypothesis inside the conformal window, we probe conformal behavior driven by a single anomalous mass dimension under the assumption of unbroken chiral symmetry at vanishing fermion mass. Our results at fixed gauge coupling, based on the assumptions of the two hypotheses we define, show low level of confidence in the conformal scenario with leading order scaling analysis. Relaxing the important assumption of leading mass-deformed conformality with its conformal finite size scaling would require added theoretical understanding of the scaling violation terms in the conformal analysis and a comprehensive test of its effects on the confidence level of the fits. Results for the running coupling, based on the force between static sources, and preliminary indications for the finite temperature transition are also presented. Staggered lattice fermions with stout-suppressed taste breaking are used throughout the simulations.     

On the excited quarks and leptons

Using a duality-like finite energy sum rule, we discuss the assumption of having excited fermions at the W scale in a supersymmetric(SUSY) and non-supersymmetric hypercolour theory where quarks and leptons are bound states of fermion and scalar preon constituents. We conclude that a SUSY-like composite model cannot have excited fermions having a mass smaller than 0.5 TeV. A non-SUSY composite model having composite fermions but elementary W bosons can produce an excited fermion mass of the order of M_W provided that the scalar vacuum condensate is of the order of the (TeV)² scale of compositeness.     

Family unification within SO(15)

We present a model for the unification of fermion families based on the gauge symmetry SO(15). It is a minimal SO(n) model which can accommodate the known fermions within a single irreducible representation. The model predicts four ordinary fermion families and four families of mirror fermions. The latter have V + A weak interactions, and their mass scale is predicted to be 10² GeV/c². We argue that radiative corrections to the fermion masses can cause non-negligible mixing between ordinary and mirror fermions. The implications of these mixings for the weak interaction phenomenology and solar neutrinos are discussed.     

Higgs boson production at CLIC in SUSY models with hierarchy of the vacuum expectation values

Many theoretical schemes predict the existence of unconventional quarks and leptons not fitting the standard pattern of fermion families. We consider two possible kinds of non-standard fermions, mirror fermions and exceptional fermions. Mirror fermions arise in a variety of models ranging from family unification to extended supersymmetry and Kaluza-Klein theories; exceptional fermions come along with the groupE ₆ which is believed to be the low energy gauge symmetry of the superstring theory. We discuss some physical properties of these non-standard particles relevant for the LEP     

Massless composites with massive constituents

We construct model field theories in which a confining gauge interaction binds massive elementary fermions into massless composite particles. The massless composites are either Goldstone bosons or $\text{spin}\text{-}\text{1}\text{2}$ fermions. In these models, the manner in which exact chiral symmetries are realized changes at a critical value of the elementary fermion mass of order (e²/16π²)Λ, where Λ is the confinement scale and e is a weak gauge coupling.