Staggered fermions for chiral gauge theories: Test on a two-dimensional axial-vector model

Böck, Wolfgang; Smit, Jan; Vink, Jeroen C.

doi:10.1016/0550-3213(94)90422-7

Cited by 12 publications

(17 citation statements)

References 18 publications

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“…In this sense the action studied in [7] has less gauge symmetry breaking than the 'canonical action' (4.3) studied here (notice that the value in ref. [7] had been normalized to one flavor). Below we shall obtain τ again from the energy density of the ground state.…”

Section: Discussionmentioning

confidence: 91%

“…The coefficient τ of the counterterm of the axial model can be obtained from the lattice vacuum polarization diagrams along the lines in ref. [7], which gives…”

Section: Discussionmentioning

confidence: 99%

“…[7] for a somewhat different but equivalent action. In this sense the action studied in [7] has less gauge symmetry breaking than the 'canonical action' (4.3) studied here (notice that the value in ref. [7] had been normalized to one flavor).…”

Section: Discussionmentioning

confidence: 99%

“…These are somewhat arbitrary because they do not correspond to symmetries of the action, although natural choices exist [7]. It has been shown in ref.…”

Section: Axial and Vector Qed In The Continuummentioning

confidence: 99%

“…We also remark that its resolution should not depend on alternative definitions of the fermion number current, constructed such that their divergence has the right anomaly (see e.g. [6,7]). Once the action and measure in the path integral are defined nonperturbatively, the stage is set, and we should just have to see what physics emerges.…”

Section: Introductionmentioning

confidence: 99%

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Fermion production despite fermion number conservation

1995

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Lattice proposals for a nonperturbative formulation of the Standard Model easily lead to a global U(1) symmetry corresponding to exactly conserved fermion number. The absence of an anomaly in the fermion current would then appear to inhibit anomalous processes, such as electroweak baryogenesis in the early universe. One way to circumvent this problem is to formulate the theory such that this U(1) symmetry is explicitly broken. However we argue that in the framework of spectral flow, fermion creation and annihilation still in fact occurs, despite the exact fermion number conservation. The crucial observation is that fermions are excitations relative to the vacuum, at the surface of the Dirac sea. The exact global U(1) symmetry prohibits a state from changing its fermion number during time evolution, however nothing prevents the fermionic ground state from doing so. We illustrate our reasoning with a model in two dimensions which has axial-vector couplings, first using a sharp momentum cutoff, then using the lattice regulator with staggered fermions. The difference in fermion number between the time evolved state and the ground state is indeed in agreement with the anomaly. A study of the vacuum energy shows that the perturbative counterterm needed for restoration of gauge invariance is insufficient in a nonperturbative setting. For reference we also study a closely related model with vector couplings, the Schwinger model, and we examine the emergence of the θ-vacuum structure of both theories.

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Section: Discussionmentioning

confidence: 91%

“…The coefficient τ of the counterterm of the axial model can be obtained from the lattice vacuum polarization diagrams along the lines in ref. [7], which gives…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…These are somewhat arbitrary because they do not correspond to symmetries of the action, although natural choices exist [7]. It has been shown in ref.…”

Section: Axial and Vector Qed In The Continuummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fermion production despite fermion number conservation

1995

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Lattice chiral fermions

Shamir¹

1996

Nuclear Physics B - Proceedings Supplements

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A lattice formulation of chiral gauge theories

Bodwin

1997

Nuclear Physics B - Proceedings Supplements

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We present a method for formulating gauge theories of chiral fermions in lattice field theory. The method makes use of a Wilson mass to remove doublers. Gauge invariance is then restored by modifying the theory in two ways: the magnitude of the fermion determinant is replaced with the square root of the determinant for a fermion with vector-like couplings to the gauge field; a double limit is taken, in which the lattice spacing associated with the fermion field is sent to zero before the lattice spacing associated with the gauge field.The method applies only to theories whose fermions are in an anomaly-free representation of the gauge group. We also present a related technique for computing matrix elements of operators involving fermion fields. Although the analyses of these methods are couched in weak-coupling perturbation theory, it is argued that the computational prescriptions are gauge invariant in the presence of a nonperturbative gauge-field configuration.

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Staggered fermions for chiral gauge theories: Test on a two-dimensional axial-vector model

Cited by 12 publications

References 18 publications

Fermion production despite fermion number conservation

Fermion production despite fermion number conservation

Lattice chiral fermions

A lattice formulation of chiral gauge theories

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