Topological charge and the spectrum of exactly massless fermions on the lattice

Chiu, Ting‐Wai

doi:10.1103/physrevd.58.074511

Cited by 63 publications

(79 citation statements)

References 36 publications

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“…The sum rule (2.11) corresponds to the one found in Ref. [6] for the special case of Dirac operators which satisfy the GW relation (1.1).…”

Section: Properties From Spectral Representationmentioning

confidence: 60%

More chiral operators on the lattice

Kerler

2002

Nuclear Physics B

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Instead of the Ginsparg-Wilson (GW) relation we only require generalized chiral symmetry and show that this results in a larger class of Dirac operators describing massless fermions, which in addition to GW fermions and to the ones proposed by Fujikawa includes many more general ones. The index turns out to depend solely on a basic unitary operator. We use spectral representations to analyze the new class and to obtain detailed properties. We also show that our weaker conditions still lead properly to Weyl fermions and to chiral gauge theories.

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“…The sum rule (2.11) corresponds to the one found in Ref. [6] for the special case of Dirac operators which satisfy the GW relation (1.1).…”

Section: Properties From Spectral Representationmentioning

confidence: 60%

More chiral operators on the lattice

Kerler

2002

Nuclear Physics B

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“…Then the effective action without fermion sources is given by 25) and its variation under eq. (2.21) is given by…”

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confidence: 99%

CP breaking in lattice chiral gauge theories

Fujikawa¹,

Ishibashi²,

Suzuki³

2002

J. High Energy Phys.

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The CP symmetry is not manifestly implemented for the local and doubler-free Ginsparg-Wilson operator in lattice chiral gauge theory. We precisely identify where the effects of this CP breaking appear. We show that they appear in: (I) Overall constant phase of the fermion generating functional. (II) Overall constant coefficient of the fermion generating functional. (III) Fermion propagator appearing in external fermion lines and the propagator connected to Yukawa vertices. The first effect appears from the transformation of the path integral measure and it is absorbed into a suitable definition of the constant phase factor for each topological sector; in this sense there appears no "CP anomaly". The second constant arises from the explicit breaking in the action and it is absorbed by the suitable weights with which topological sectors are summed. The last one in the propagator is inherent to this formulation and cannot be avoided by a mere modification of the projection operator, for example, in the framework of the Ginsparg-Wilson operator. This breaking emerges as an (almost) contact term in the propagator when the Higgs field, which is treated perturbatively, has no vacuum expectation value. In the presence of the vacuum expectation value, however, a completely new situation arises and the breaking becomes intrinsically non-local, though this breaking may still be removed in a suitable continuum limit. This non-local CP breaking is expected to persist for a non-perturbative treatment of the Higgs coupling.

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“…The eigenvalues of D ov are lying on a circle in the complex plane with center at (m 0 , 0) and radius of length m 0 , consisting of complex eigenmodes in conjugate pairs, and (for topologically nontrivial gauge background) real eigenmodes with eigenvalues at 0 and 2m 0 satisfying the chirality sum rule, n + − n − + N + − N − = 0 [10], where n ± (N ± ) denote the number of eigenmodes at 0 (2m 0 ) with ± chirality. Empirically, the real eigenmodes always satisfy either (n + = N − , n − = N + = 0) or (n − = N + , n + = N − = 0).…”

Section: Projection Of the Low-lying Eigenmodes Of The Overlap-dirac mentioning

confidence: 99%