Lattice 2001: Reflections

Hasenfratz, P.

doi:10.1016/s0920-5632(01)01655-3

Cited by 35 publications

(50 citation statements)

References 111 publications

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“…Finally we remark that in the n = 3 case it would be nice to know also the three-loop coefficient r (3) , however it would require a lot more effort to compute. This is built from (among other things) the two-loop coefficient c (2) 1 appearing in the effective action and the three-loop anomalous dimension matrix elements ν (3) ij .…”

Section: The Final Resultsmentioning

confidence: 99%

The puzzle of apparent linear lattice artifacts in the 2d non-linear σ-model and Symanzik's solution

2010

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Lattice artifacts in the 2d O(n) non-linear σ-model are expected to be of the form O(a 2 ), and hence it was (when first observed) disturbing that some quantities in the O(3) model with various actions show parametrically stronger cutoff dependence, apparently O(a), up to very large correlation lengths. In a previous letter [1] we described the solution to this puzzle. Based on the conventional framework of Symanzik's effective action, we showed that there are logarithmic corrections to the O(a 2 ) artifacts which are especially large (ln 3 a) for n = 3 and that such artifacts are consistent with the data. In this paper we supply the technical details of this computation. Results of Monte Carlo simulations using various lattice actions for O(3) and O(4) are also presented.

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Section: The Final Resultsmentioning

confidence: 99%

The puzzle of apparent linear lattice artifacts in the 2d non-linear σ-model and Symanzik's solution

2010

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“…The index of D then gets I = N + (1) − N − (1), which thus is given by (8) and subject to (7). For G andḠ analogous representations to (11) hold with spectal functions g andḡ, respectively.…”

Section: General Relationsmentioning

confidence: 99%

General chiral gauge theories

Kerler

2004

Nuclear Physics B - Proceedings Supplements

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Only requiring that Dirac operators decribing massless fermions on the lattice decompose into Weyl operators we arrive at a large class of them. After deriving general relations from spectral representations we study correlation functions of Weyl fermions for any value of the index, stressing the related conditions for basis transformations and getting the precise behaviors under gauge and CP transformations. Using the detailed structure of the chiral projections we also obtain a form of the correlation functions with a determinant in the general case.

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“…Namely, it is impossible to maintain the manifest invariance of the local and chiral Lagrangian under the CP transformation [1,2].…”

Section: Cp Symmetry In Chiral Gauge Theorymentioning

confidence: 99%

“…This is again interpreted as a change of representation of chiral projection operators, from P ± andP ± to γ 5P± γ 5 and P ± , constructed from a vector-like Ginsparg-Wilson theory if one introduces two sets of fermion fields ψ (1) and ψ (2) in eq. (4.1)…”

Section: Cp (Or C) Transformation and Yukawa Couplingsmentioning

confidence: 99%

“…It has been recently shown that CP symmetry in chiral gauge theory [1,2,3] and also the Majorana reduction in the presence of chiral symmetric Yukawa couplings [4] have a certain conflict with lattice chiral symmetry, doubler-free and locality conditions in the framework of Ginsparg-Wilson operators [5]- [19]. There exists a closely related formulation of lattice fermions which is called the domain wall fermion [20]- [26].…”

Section: Introductionmentioning

confidence: 99%

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Domain wall fermion andCPsymmetry breaking

Fujikawa

Suzuki

2003

Phys. Rev. D

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We examine the CP properties of chiral gauge theory defined by a formulation of the domain wall fermion, where the light field variables q andq together with Pauli-Villars fields Q andQ are utilized. It is shown that this domain wall representation in the infinite flavor limit N = ∞ is valid only in the topologically trivial sector, and that the conflict among lattice chiral symmetry, strict locality and CP symmetry still persists for finite lattice spacing a. The CP transformation generally sends one representation of lattice chiral gauge theory into another representation of lattice chiral gauge theory, resulting in the inevitable change of propagators. A modified form of lattice CP transformation motivated by the domain wall fermion, which keeps the chiral action in terms of the Ginsparg-Wilson fermion invariant, is analyzed in detail; this provides an alternative way to understand the breaking of CP symmetry at least in the topologically trivial sector. We note that the conflict with CP symmetry could be regarded as a topological obstruction. We also discuss the issues related to the definition of Majorana fermions in connection with the supersymmetric Wess-Zumino model on the lattice.

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Lattice 2001: Reflections

Abstract: A few subjects which strongly intertwine our field are discussed: K → ππ decay, chiral symmetry on the lattice and a few other selected topics. Open questions are touched also on perturbation theory, locality, Gribov copies, CP symmetry in chiral gauge theories and cut-off effects.

Cited by 35 publications

References 111 publications

The puzzle of apparent linear lattice artifacts in the 2d non-linear σ-model and Symanzik's solution

The puzzle of apparent linear lattice artifacts in the 2d non-linear σ-model and Symanzik's solution

General chiral gauge theories

Domain wall fermion andCPsymmetry breaking

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