Further discussions on a possible lattice chiral gauge theory (original) (raw)

A Possible Lattice Chiral Gauge Theory

1996

We analyze the dynamics of an SU L (2)⊗U R (1) chiral gauge theory on a lattice with a large multifermion coupling 1 ≪ g 2 < ∞. It is shown that no spontaneous symmetry breaking occurs; the "spectator" fermion ψ R (x) is a free mode; doublers are decoupled as massive Dirac fermions consistently with the chiral gauge symmetry. Whether right-handed three-fermion states disappear and chiral fermions emerge in the low-energy limit are discussed. Provided right-handed three-fermion states disappear, we discuss the chiral gauge coupling, Ward identities, the gauge anomaly and anomalous U L (1) global current within the gaugeinvariant prescription of renormalization of the gauge perturbation theory.

A Lattice Chiral Gauge Theory with Multifermion Couplings

Eprint Arxiv Hep Lat 9510043, 1995

Analyzing an SU L (2)-chiral gauge theory with external multifermion couplings, we find a possible scaling region where doublers decouple by acquiring chiral-invariant masses and ψ R is free mode owing to the ψ R-shift-symmetry, the chiral continuum theory of ψ L can be defined. This is not in agreement with the general belief of the failure of theories so constructed .

Chiral fermions on the lattice

Nuclear Physics B, 1995

The overlap approach to chiral gauge theories on arbitrary D-dimensional lattices is studied. The doubling problem and its relation to chiral anomalies for D = 2 and 4 is examined. In each case it is shown that the doublers can be eliminated and the well known perturbative results for chiral anomalies can be recovered. We also consider the multi-flavour case and give the general criteria for the construction of anomaly free chiral gauge theories on arbitrary lattices. We calculate the second order terms in a continuum approximation to the overlap formula in D dimensions and show that they coincide with the bilinear part of the effective action of D-dimensional Weyl fermions coupled to a background gauge field. Finally, using the same formalism we reproduce the correct Lorentz, diffeomorphism and gauge anomalies in the coupling of a Weyl fermion to 2-dimensional gravitational and Maxwell fields.

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 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.

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.

Undoubled chiral fermions on a lattice

Nuclear Physics B - Proceedings Supplements, 1997

We analyze the dynamics of an SUL(2)⊗UR(1) chiral theory on the lattice with a strong multifermion coupling. It is shown that no spontaneous symmetry breaking occurs; the "spectator" fermion ψR is a free mode; doublers are decoupled as massive Dirac fermions consistently with the chiral symmetries. In 1+1 dimension, we show that the right-handed three-fermion state disappears at the threshold and an undoubled left-handed chiral fermion remains in the continuum limit.

Vanishing of the Anomaly in Lattice Chiral Gauge Theory

Annales Henri Poincaré

The anomaly cancellation is a basic property of the Standard Model, crucial for its consistence. We consider a lattice chiral gauge theory of massless Wilson fermions interacting with a non-compact massive U(1) field coupled with left- and right-handed fermions in four dimensions. We prove in the infinite volume limit, for weak coupling and inverse lattice step of the order of boson mass, that the anomaly vanishes up to subleading corrections and under the same condition as in the continuum. The proof is based on a combination of exact Renormalization Group, non-perturbative decay bounds of correlations and lattice symmetries.