Chiral analog gauge theories on the lattice

We discuss a class of lattice gauge theories with fermions that have properties in common with continuum chiral gauge theories. The symmetries we gauge have often been mistaken for chiral symmetries in the literature. We show that in the continuum limit they converge to ordinary vector-like symmetries, but that at strong coupling they behave like chiral symmetries. We find lattice analogs of the technicolor mechanism and of the generation of composite massless fermions in chiral gauge theories.     

The effective action for chiral fermions

We present an exact formula for the imaginary part of the effective action for chiral fermions in complex representations of the gauge group G, in the presence of an arbitrary external gauge field configuration. This result provides a unified treatment of both local and global anomalies and a precise characterization of some of the special properties of chiral fermions.     

Non-perturbative decoupling theorems in lattice gauge theory simulations

We illustrate that massless fermions which condense at high energy decouple from low energy sectors of a gauge theory by considering a lattice theory with (almost) massless quarks in the fundamental and adjoint representations of the gauge group. We confirm that the low energy chiral condensate of the fundamental fermions satisfies the asymptotic freedom scaling law with the adjoint fermions decoupled.     

Domain wall fermions with Majorana couplings

We examine the lattice boundary formulation of chiral fermions with either an explicit Majorana mass or a Higgs-Majorana coupling introduced on one of the boundaries. We demonstrate that the low-lying spectrum of the models with an explicit Majorana mass of the order of an inverse lattice spacing is chiral at tree level. Within a mean-field approximation we show that the systems with a strong Higgs-Majorana coupling have a symmetric phase, in which a Majorana mass of the order of an inverse lattice spacing is generated without spontaneous breaking of the gauge symmetry. We argue, however, that the models within such a phase have a chiral spectrum only in terms of the fermions that are singlets under the gauge group. The application of such systems to non-perturbative formulations of supersymmetric and chiral gauge theories is briefly discussed.     

Composite massless fermions in strongly coupled lattice gauge theories

We show that a class of strongly coupled lattice gauge theories with fermions in real representations of the gauge group do not have chiral symmetry breaking. The resulting spectrum of massless composite fermions satisfies 't Hooft's constraints if the model is naively extrapolated to the continuum limit. We argue that it is in fact the correct spectrum of the continuum gauge theory.     

Chiral bosonization in non-abelian gauge theories

The chiral bosonization in non-abelian gauge theories is described starting directly from the QCD functional. For a given mass scale Λ, QCD may be equivalently represented by colour chiral fields, gauge fields and high energy fermions. The effective action for colour chiral fields may admit the existence of a colour skyrmion-boson with baryon number 2/3.     

A numerical study of lattice QED with dynamical fermions

Using the pseudo-fermion method U(1) lattice gauge theory with dynamical staggered fermions is studied. The plaqette energy, the chiral order parameter and the Polyakov line have been measured. With fermions of mass 0.20 and 0.25 a phase transition is observed, separating the strong coupling regime from a phase where chiral symmetry is restored.     

Gauge anomaly cancellation in chiral gauge theories

We consider chiral fermions interacting minimally with abelian and non-abelian gauge fields. Using a path integral approach and exploring the consequences of a mechanism of symmetry restoration, we show that the gauge anomaly has null expectation value in the vacuum for both cases (abelian and non-abelian). We argue that the same mechanism has no possibility to cancel the chiral anomaly, what eliminates competition between chiral and gauge symmetry at full quantum level. We also show that the insertion of the gauge anomaly in arbitrary gauge invariant correlators gives a null result, which points towards anomaly cancellation in the subspace of physical state vectors.     

The phase structure of Einstein–Cartan theory

In the Einstein–Cartan theory of torsion-free gravity coupling to massless fermions, the four-fermion interaction is induced and its strength is a function of the gravitational and gauge couplings, as well as the Immirzi parameter. We study the dynamics of the four-fermion interaction to determine whether effective bilinear terms of massive fermion fields are generated. Calculating one-particle-irreducible two-point functions of fermion fields, we identify three different phases and two critical points for phase transitions characterized by the strength of four-fermion interaction: (1) chiral symmetric phase for massive fermions in strong coupling regime; (2) chiral symmetric broken phase for massive fermions in intermediate coupling regime; (3) chiral symmetric phase for massless fermions in weak coupling regime. We discuss the scaling-invariant region for an effective theory of massive fermions coupled to torsion-free gravity in the low-energy limit.     

Anomaly driven signatures of new invisible physics at the Large Hadron Collider

Many extensions of the Standard Model (SM) predict new neutral vector bosons at energies accessible by the Large Hadron Collider (LHC). We study an extension of the SM with new chiral fermions subject to non-trivial anomaly cancellations. If the new fermions have SM charges, but are too heavy to be created at LHC, and the SM fermions are not charged under the extra gauge field, one would expect that this new sector remains completely invisible at LHC. We show, however, that a non-trivial anomaly cancellation between the new heavy fermions may give rise to observable effects in the gauge boson sector that can be seen at the LHC and distinguished from backgrounds.     

CN REALIZATION OF THE CHIRAL SYMMETRY IN THE LATTICE GAUGE THEORY CONTAINING THE U(I) CHIRAL GAUGE FIELD

We investigate the lattice gauge theory with a gauge group UxV(1) where U is a non-Abelian group and V(1) is a chiral Abelian group.In the strong coupling approximation for the U gauge field we find that the V(1) chiral symmetry is realized through parity doublets of composite fermions for strong V(1) coupling and that it is spontaneousely broken through a techni color-like mechanism for weak V(1) coupling.     

Anomalous commutators in two-dimensional chiral gauge theories

It is shown that in two-dimensional models of chiral fermions coupled with background gauge fields, anomalous commutators of currents as well as of generators of time-independent gauge transformations are completely determined by the anomaly if the gauge group is semisimple. The four-dimensional case is commented on.     

The derivative expansion of the fermion number current

The fermion number current is evaluated to leading order in the derivative expansion for chiral fermions in the background of arbitrary Higgs and chiral gauge fields. This current is given by the gauge topological current plus a total divergence term. The total divergence term is absent in Weinberg-Salam theory with one scalar Higgs doublet, even for an arbitrary mass matrix, but appears when several Higgs doublets are present.     

On the cancellation of fermion loops in chiral gauge theories in (1+1) dimensions

We show that for chiral gauge theories in (1+1) dimensions, with the gauge field coupling only to left(right)-handed fermions, the fermion loop contributions cancel in the vacuum expectation value of gauge invariant quantities, if the regularization of the theory respects the left(right)-handed coupling.     

Variational Study of 〈ψψ〉 in the Lattice Schwinger Model with Wilson Fermions

We used the variational method in lattice gauge theory to calculate the chiral order parameter 〈ψψ〉 in the Schwinger model with Wilson fermions.     

A chiral invariant decoupling of replica lattice fermions

A chiral invariant lattice fermion action which solves the species-doubling problem of Dirac fermions on a lattice for (even) dimensions of space-time less than eight is presented. The decoupling of replica fermions requires to give up rotational and gauge symmetry in the regularization procedure. The corresponding lattice Schwinger model reproduces all the results of the continuum theory.     

Bott periodicity and realizations of chiral symmetry in arbitrary dimensions

We compute the chiral symmetries of the Lagrangian for confining “vector-like” gauge theories with massless fermions in d-dimensional Minkowski space and, under a few reasonable assumptions, determine the form of the quadratic fermion condensates which arise through spontaneous breaking of these symmetries. We find that for each type (complex, real, or pseudoreal) of representation of the gauge group carried by the fermions, the chiral symmetries of the Lagrangian, as well as the residual symmetries after dynamical breaking, exactly follow the pattern of Bott periodicity as the dimension changes. The consequences of this for the topological features of the low-energy effective theory are considered.     

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.     

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.     

Commutator of gauge generators in non-abelian chiral theory

Commutators among non-abelian fermion currents are calculated using the BJL limit. The relation between the covariant seagull and the gauge dependence of the fermion current is derived for a canonical non-abelian theory using the path integral formulation. We observe that in a non-abelian theory with coupling to chiral fermions this relation is violated and this produces a non-trivial commutator of gauge group generators.