Topical results on lattice chiral fermions in the CFA (original) (raw)

Lattice chiral schwinger model in the continuum formulation

Nuclear Physics B - Proceedings Supplements, 1998

We pursue further an approach to lattice chiral fermions in which the fermions are treated in the continuum. To render the effective action gauge invariant, counterterms have to be introduced. We determine the counterterms for smooth gauge fields, both analytically and numerically. The final result is that the imaginary part of the effective action can be computed analytically from the lattice gauge field, while the real part is given by one half of the action of the corresponding vector model.

A method for putting chiral fermions on the lattice

Nuclear Physics B - Proceedings Supplements, 1993

We describe a method to put chiral gauge theories on the lattice. Our method makes heavy use of the effective action for chiral fermions in the continuum, which is in general complex. As an example we discuss the chiral Schwinger model.

A streamlined method for chiral fermions on the lattice

Nuclear Physics B - Proceedings Supplements, 1993

We discuss the use of renormalization counterterms to restore the chiral gauge symmetry in a lattice theory of Wilson fermions. We show that a large class of counterterms can be implemented automatically by making a simple modification to the fermion determinant.

Lattice Schwinger model: Confinement, anomalies, chiral fermions, and all that

Physical Review D, 2000

In order to better understand what to expect from numerical CORE computations for two-dimensional massless QED (the Schwinger model) we wish to obtain some analytic control over the approach to the continuum limit for various choices of fermion derivative. To this end we study the Hamiltonian formulation of the lattice Schwinger model (i.e., the theory defined on the spatial lattice with continuous time) in A 0 = 0 gauge. We begin with a discussion of the solution of the Hamilton equations of motion in the continuum, we then parallel the derivation of the continuum solution within the lattice framework for a range of fermion derivatives. The equations of motion for the Fourier transform of the lattice charge density operator show explicitly why it is a regulated version of this operator which corresponds to the pointsplit operator of the continuum theory and the sense in which the regulated lattice operator can be treated as a Bose field. The same formulas explicitly exhibit operators whose matrix elements measure the lack of approach to the continuum physics. We show that both chirality violating Wilson-type and chirality preserving SLAC-type derivatives correctly reproduce the continuum theory and show that there is a clear connection between the strong and weak coupling limits of a theory based upon a generalized SLAC-type derivative.

Further discussions on a possible lattice chiral gauge theory

Physics Letters B, 1997

In a possible SU L (2) lattice chiral gauge theory with a large multifermion coupling, we try to further clarify the threshold phenomenon: the possibility that the right-handed three-fermion state turns into the virtual states of its constituents (free chiral fermions) in the low-energy limit. Provided this phenomenon occurs, we discuss the chiral gauge coupling, Ward identities and the gauge anomaly within the gauge-invariant prescription of the perturbative chiral gauge theory.

Further study of the possible scaling region of lattice chiral fermions

Physical Review D, 2000

In the possible scaling region for an SU (2) lattice chiral fermion advocated in Nucl. Phys. B486 (1997) 282, no hard spontaneous symmetry breaking occurs and doublers are gauge-invariantly decoupled via mixing with composite three-fermion-states that are formed by local multifermion interactions. However the strong coupling expansion breaks down due to no "static limit" for the low-energy limit (pa ∼ 0). In both neutral and charged channels, we further analyze relevant truncated Green functions of three-fermion-operators by the strong coupling expansion and analytical continuation of these Green functions in the momentum space. It is shown that in the low-energy limit, these relevant truncated Green functions of three-fermion-states with the "wrong" chiralities positively vanish due to the generalized form factors (the wave-function renormalizations) of these composite three-fermion-states vanishing as O((pa) 4) for pa ∼ 0. This strongly implies that the composite three-fermion-states with "wrong" chirality are "decoupled" in this limit and the low-energy spectrum is chiral, as a consequence, chiral gauge symmetries can be exactly preserved.

3 Into 2 Doesn't Go: (almost) chiral gauge theory on the lattice

1993

Kaplan recently proposed a novel lattice chiral gauge theory in which the bare theory is defined on (2n+1)(2n+1)(2n+1)-dimensions, but the continuum theory emerges in 2n2n2n-dimensions. We explore whether the resulting theory reproduces all the features of continuum chiral gauge theory in the case of two-dimensional axial Schwinger model. We find that one can arrange for the two-dimensional perturbation expansion to be reproduced successfully. However, the theory fails to reproduce the 2-dimensional fermion nonconservation.

A possible scaling region of chiral fermions on a lattice

Nuclear Physics B, 1997

We present the details of analyzing an SU L (2) ⊗ U R (1) chiral theory with multifermion couplings on a lattice. An existence of a possible scaling region in the phase space of multifermion couplings for defining the continuum limit of chiral fermions is advocated. In this scaling region, no spontaneous symmetry breaking occurs; the "spectator" fermion ψ R (x) is a free mode and decoupled; doublers are decoupled as massive Dirac fermions consistently with the SU L (2) ⊗ U R (1) chiral symmetry, whereas the normal mode of ψ i L (x) is plausibly speculated to be chiral in the continuum limit. This is not in agreement with the general belief of the definite failure of theories so constructed.

A lattice chiral theory with multifermion couplings

Physics Letters B, 1996

Analyzing an SU L (2) ⊗ U R (1) chiral theory with multifermion couplings on a lattice, we find a possible region in the phase space of multifermion couplings, where no spontaneous symmetry breaking occurs, doublers are decoupled as massive Dirac fermions consistently with the SU L (2) ⊗ U R (1) chiral symmetry, the "spectator" fermion ψ R (x) is free mode, whereas the normal mode of ψ i L (x) is plausibly speculated to be chiral in the continuum limit. This is not in agreement with the general belief of the definite failure of theories so constructed.