Analytic progress on exact lattice chiral symmetry

Kikukawa, Yoshio

doi:10.1016/s0920-5632(01)01645-0

Cited by 7 publications

(4 citation statements)

References 62 publications

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“…As a result, we have 19) and the difference, θ[U; 2 − t] − θ[U; t], if it exists, is a constant: 20) where the constant θ M is assigned for each topological sector M, U ∈ M. 15 The dimensionality of fermionic spaces before and after CP transformation is however different,…”

Section: Cp Transformed Generating Functional 41 Generating Functionmentioning

confidence: 99%

“…(5.3) and (5.8). 19 The remarkable fact is that these conditions are invariant under t → 2 − t. Thus, if we have an ideal measure term L η [U; t] which works for U with respect to γ . Therefore, we may set without loss of generality…”

Section: Invariance Under T → 2 − T and The Cp Property Of The Measur...mentioning

confidence: 99%

“…However, the condition (2.16) alone does not specify the fermion measure uniquely and there is an ambiguity of the phase. For two different choices of basis, {v, v} and {w, w}, we have 19) where the phase is given by the Jacobian for the change of basis 20) where…”

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confidence: 99%

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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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Section: Cp Transformed Generating Functional 41 Generating Functionmentioning

confidence: 99%

Section: Invariance Under T → 2 − T and The Cp Property Of The Measur...mentioning

confidence: 99%

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CP breaking in lattice chiral gauge theories

Fujikawa¹,

Ishibashi²,

Suzuki³

2002

J. High Energy Phys.

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“…A large volume of work has followed since. The reader is referred to the annual reviews [7,8,9,10,11,12,13,14,15,16] and references therein. The DWF lattice regulator begins by defining a massive Wilson fermion [17] in 2n + 1 dimensions.…”

Section: Introductionmentioning

confidence: 99%

Staggered domain wall fermion method

Fleming

Vranas

2002

Phys. Rev. D

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A different lattice fermion method is introduced. Staggered domain wall fermions are defined in 2n + 1 dimensions and describe 2 n flavors of light lattice fermions with exact U(1)×U(1) chiral symmetry in 2n dimensions. As the size of the extra dimension becomes large, 2 n chiral flavors with the same chiral charge are expected to be localized on each boundary and the full SU(2 n )×SU(2 n ) flavor chiral symmetry is expected to be recovered. SDWF give a different perspective into the inherent flavor mixing of lattice fermions and by design present an advantage for numerical simulations of lattice QCD thermodynamics. The chiral and topological index properties of the SDWF Dirac operator are investigated. And, there is a surprise ending...

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