A two-Higgs doublet model with remarkable CP properties

We analyze generalized CP symmetries of two-Higgs doublet models, extending them from the scalar to the fermion sector of the theory. We show that, other than the usual CP transformation, there is only one of those symmetries which does not imply massless charged fermions. That single model which accommodates a fermionic mass spectrum compatible with experimental data possesses a remarkable feature. Through a soft breaking of the symmetry it displays a new type of spontaneous CP violation, which does not occur in the scalar sector responsible for the symmetry breaking mechanism but, rather, in the fermion sector.     

Physical charged fermions in the fermion-monopole system

In order to demonstrate existence of physical charged fermions in the system consisting of a doublet of J = 0 massless fermions coupled to the radial electric field in the presence of a point-like SU(2) monopole, it is shown that the system is equivalent to that of a doublet of two-dimensional massless fermions carrying renormalized charges. As a consequence, it follows that charges are quantized if we confine ourselves to Fock space of the free massless fermion fields.     

Localization of matters on the bent brane in bulk

We investigate the possibility of localizing various matter fields on a bent AdS₄ (dS₄) thick brane in AdS₅. For spin 0 scalar field, we find a massless zero mode and an excited state which can be localized on the bent brane. For spin 1 vector field, there is only a massless zero mode on the bent brane. For spin 1/2 fermion field, it is shown that, in the case of no Yukawa coupling of scalar-fermion, there is no existence of localized massless zero mode for both left and right chiral fermions. In order to localize massless fermions, some kind of Yukawa coupling must be included. We study two types of Yukawa couplings as examples. Localization property of chiral fermions is related to the parameters of the brane model, the Yukawa coupling constant and the cosmological constant of the 4-dimensional space–time.     

Infrared problem and boson suppression in massless Abelian gauge theory

The vacuum polarization effects lead to a complete shielding of the charge and to a suppression of real boson excitations in massless Abelian gauge theory. Nevertheless, fermions interact by means of neutral vector currents. It is concluded that charged massless fermions cannot exist.     

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.     

Flavour and superunification

We consider the possibility of a non-trivial embedding of $\text{(}\text{10}\text{+}\text{5}\text{)}\text{SU}\text{(5)}$ families of spin if$\text{1}\text{2}$ left-handed fermions in a combination of irreducible massless supermultiplets of N extended supersymmetry. We demand the whole spectrum of spin $\text{1}\text{2}$ states to be anomaly free with respect to SU(N). This turns out to be a necessary condition for the absence of anomalies at the SU(5) level. We find two classes of models, with spin $\text{1}\text{2}$ fermions in SU(N) representations associated to one- and two-column Young tableaux, respectively, in which each irreducible massless multiplet occurs at most once. These two classes of models lead to a nontrivial family generation due to supersymmetry. For N = 8 extended supersymmetry, they give at most three and five families, respectively. The first class of models is more natural in the way it excludes SU(5) exotics. The same analysis is extended to the massless multiplets that can be obtained from bilinear composite fields of the (preonic) elementary fields of N extended supergravity. We prove that the generation of families requires the repetition of massless multiplets and that ($\text{10 +}\text{5}$) SU(5) families can only be generated in pairs. General properties of multilinear composite operators of the preonic fields are given and the rôle of massive representations to classify towers of operators with definite spin is pointed out.     

Light composite fermions

In this paper we consider the possibility that QCD-like theories can lead to massless or near-massless composite fermions. The method of analysis relies on a conjectured equivalence between the confined and Higgs phases of certain non-abelian gauge theories. This “complementarity” principle allows us to analyze a theory as if the Higgs phenomenon occurred and then reinterpret the results in the language of composite gauge singlets. Those fermions which remain massless in the Higgs picture may then be interpreted as massless fermionic composites.The principle of complementarity, when applied to a class of extended technicolor models, implies that quarks and leptons are composites bound at a scale of order 1–100 TeV.     

New generation of massless Dirac fermions in graphene under external periodic potentials

We show that new massless Dirac fermions are generated when a slowly varying periodic potential is applied to graphene. These quasiparticles, generated near the supercell Brillouin zone boundaries with anisotropic group velocity, are different from the original massless Dirac fermions. The quasiparticle wave vector (measured from the new Dirac point), the generalized pseudospin vector, and the group velocity are not collinear. We further show that with an appropriate periodic potential of triangular symmetry, there exists an energy window over which the only available states are these quasiparticles, thus providing a good system to probe experimentally the new massless Dirac fermions. The required parameters of external potentials are within the realm of laboratory conditions.     

Eigenvalue inequalities for fermions in gauge theories

We show that QCD with a sufficient number of fermions of zero bare mass has physical massless particles. That result also follows from triangle anomalies, so only our method is novel. Our method involves proving special cases of recently conjectured paramagnetic inequalities for fermions. The proofs are simple applications of the Atiyah-Patodi-Singer theorem on spectral flow.Supported in part by the National Science Foundation Grant No. PHY80-19754Supported in part by DOE Grant No. DE-AC02-76ER02220     

On a new type of massless Dirac fermions in crystalline topological insulators

A new type of massless Dirac fermions in crystalline three-dimensional topological insulators (three-dimensional → two-dimensional situation) has been predicted. The spectrum has fourfold degeneracy at the top of the two-dimensional Brillouin zone (M point) and twofold degeneracy near the M point. Crystal symmetry along with the time reversal invariance in three-dimensional topological insulators allows fourfold degenerate Dirac cones, which are absent in the classification of topological features in R.-J. Slager et al., Nat. Phys. 9, 98 (2013). The Hamiltonian in the cited work does not contain Dirac singularities with more than twofold degeneracy. For this reason, the corresponding topological classification is incomplete. The longitudinal magnetic field in the spinless case holds the massless dispersion law of fermions and does not lift fourfold degeneracy. In the spinor case, the magnetic field lifts fourfold degeneracy, holding only twofold degeneracy, and results in the appearance of a band gap in the spectrum of fermions.     

A tool kit for builders of composite models

I motivate and discuss a dynamical picture of strong gauge interactions in a simple class of models, some of which yield massless composite fermions. I show how to put simple components together into models that can describe quarks with color and flavor.     

4d fermionic superstrings with arbitrary twists

We present the rules for systematically constructing all consistent four-dimensional string theories, using free world-sheet fermions which pick up arbitrary phases when parallel transported around the string. These rules are necessary and sufficient for multi-loop modular invariance. They lead to theories with general Z_N (GSO-type) projections, whose merits for model-building we discuss. We classify all boundary conditions yielding massless space-time spinors. We show that, in contrast to the case of only real 2d fermions, all possible realizations of world-sheet supersymmetry are now allowed. This opens the way for the construction of a new class of supersymmetric string models.     

Gravitational anomalies and Schwinger terms

A BRST transformation incorporating general coordinate, Lorentz and Weyl transformations is defined. The variation of the effective action for fermions moving in an external gravitational field is calculated using an extended BRST analysis. InD=2 dimensions the Schwinger terms appearing in the equal time commutators of energy momentum tensors are related to the gravitational and Weyl anomalies for a massless spin 0 and a massless spin 1/2 model, respectively.     

Fermion-meron interactions in Minkowski space-time

The interaction between massless isospinor fermions and a class of regular (classical) Yang-Mills fields in Minkowski space-time is analyzed. For the case in which the potential corresponds to the meron field of DeAlfaro, Fubini and Furlan the resulting Dirac equations are solved in general. Some properties of the general solution and the ensuing physical picture are briefly discussed.     

Anomalies in PT-Symmetric Quantum Field Theory

It is shown that a version of PT-symmetric electrodynamics based on an axial-vector current coupling massless fermions to the photon possesses anomalies and so is rendered nonrenormalizable. An alternative theory is proposed based on the conventional vector current constructed from massive Dirac fields, but in which the PT transformation properties of electromagnetic fields are reversed. Such a theory seems to possess many attractive features.     

Quantum criticality between topological and band insulators in 3+1 dimensions

Four-component massive and massless Dirac fermions in the presence of long range Coulomb interaction and chemical potential disorder exhibit striking fermionic quantum criticality. For an odd number of flavors of Dirac fermions, the sign of the Dirac mass distinguishes the topological and the trivial band insulator phases, and the gapless semimetallic phase corresponds to the quantum critical point that separates the two. Up to a critical strength of disorder, the semimetallic phase remains stable, and the universality class of the direct phase transition between two insulating phases is unchanged. Beyond the critical strength of disorder the semimetallic phase undergoes a phase transition into a disorder controlled diffusive metallic phase, and there is no longer a direct phase transition between the two types of insulating phases.     

Fermions and spherically symmetric monopoles

The interaction of fermions with monopoles is analyzed for general spherically symmetric monopoles of arbitrary strength and massless fermions in arbitrary representations of the gauge group. The results are based on a solution to the Dirac equation in the field of the monopole, valid in the point limit and in all partial waves. The partial waves in which non-conservation of global charges may occur are identified. A two-dimensional lagrangian is derived, which includes the Coulomb interactions generated by the complete abelian subgroup of the unbroken gauge group. The fermions are represented by a set of doublets with a boundary condition that reflects the structure of the core. We derive a simple formula for the conservation laws of this model which determine all scattering processes completely. The results have a consistent interpretation in terms of anomalies and field configurations with non-trivial winding number. We give an explicit construction of the zero modes for all helicity-violating multi-fermion condensates. The formalism is applied to several higher strength monopoles in SO(10) based models.     

General chiral gauge theories on the lattice

We still extend the large class of Dirac operators decribing massless fermions on the lattice found recently, only requiring that such operators decompose into Weyl operators. After deriving general relations and constructions of operators, we study the basis representations of the chiral projections. We then investigate correlation functions of Weyl fermions for any value of the index, stressing the related conditions for basis transformations and their consequences, and getting the precise behaviors under gauge transformations and CP transformations. Various further developments include considerations of the explicit form of the effective action and of a representation of the general correlation functions in terms of alternating multilinear forms. For comparison we also consider gauge-field variations and their respective applications. Finally we compare with continuum perturbation theory.     

I. The isotopic Foldy-Wouthuysen representation and chiral symmetry

The paper introduces the isotopic Foldy-Wouthuysen representation. This representation was used to derive equations for massive interacting fermion fields. When the interaction Hamiltonian commutes with the matrix γ⁵, these equations possess chiral invariance irrespective of whether fermions have mass or are massless. The isotopic Foldy-Wouthuysen representation preserves the vector and axial currents irrespective of the fermion mass value. In the Dirac representation, the axial current is preserved only for massless fermions. In the isotopic Foldy-Wouthuysen representation, the ground state of fermions (vacuum) turns out to be degenerate, and therefore there is the possibility of spontaneously breaking parity (P — symmetry). This study considers the example of constructing a chirally symmetric quantum electrodynamics framework in the isotopic Foldy-Wouthuysen representation. A number of physical processes are calculated in the lowest orders of the perturbation theory. Final results of the calculations agree with the results of the standard quantum electrodynamics.     

On the conservation of electric charge around a monopole of finite size

In monopole-fermion dynamics, the boundary condition which is responsible for baryon number non-conservation also violates electric and color hypercharge conservation. We show by detailed calculations that actually the latter conservation laws are dynamically restored. It is shown that for a finite size monopole, there is a small but finite amplitude for the monopole ground state to make a virtual transition into a state containing a dyon and some fermions carrying equal and opposite charge as that of the dyon. But the amplitude for this state to make a virtual transition to a state carrying a net total charge is identically zero. The monopole ground state, as a result, is an eigenstate of electric charge even in the presence of massless fermions. We also calculate the four-body charge and chirality conserving but baryon number violating condensates, which exist independently of the existence of the anomaly and hence persist even in the presence of more generations of massless fermions.