Weak coupling expansion of massless QCD with a Ginsparg-Wilson fermion and axial U(1) anomaly

Kikukawa, Yoshio; Yamada, Atsushi

doi:10.1016/s0370-2693(99)00021-0

Cited by 127 publications

(166 citation statements)

References 30 publications

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“…This is directly related to the connection with the index theorems in the continuum; for recent reviews see Adams (2000) and Kerler (2000). Recent detailed analysis (Luscher, 2000;Kikukawa and Yamada, 1999) shows that this operator is particularly well behaved order by order in perturbation theory. This has led to hopes that this may lead the way to a rigorous formulation of chiral models, such as the standard model.…”

Section: The Ginsparg-wilson Relationmentioning

confidence: 87%

Aspects of chiral symmetry and the lattice

2001

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I explore the non-perturbative issues entwining lattice gauge theory, anomalies, and chiral symmetry. After briefly reviewing the importance of chiral symmetry in particle physics, I discuss how anomalies complicate lattice formulations.Considerable information can be deduced from effective chiral Lagrangians, helping interpret the expectations for lattice models and elucidating the role of the CP violating parameter Θ. I then turn to a particularly elegant scheme for exploring this physics on the lattice. This uses an auxiliary extra space-time dimension, with the physical world being a four dimensional interface.

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Section: The Ginsparg-wilson Relationmentioning

confidence: 87%

Aspects of chiral symmetry and the lattice

2001

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“…It can be seen, for example, from the computation of chiral anomaly [38,39]. In what follows, r is fixed to the standard value r = 1.…”

Section: Lattice Formulations With Overlap Dirac Operatormentioning

confidence: 99%

“…Tr(γ 3 a D) has been computed in the two-dimensional case [38], assuming that A µ (x) appearing in the expansion of U µ (x) = e iaAµ(x) are smooth external variables. We obtain…”

Section: Q-supersymmetry Transformationmentioning

confidence: 99%

Ginsparg-Wilson Formulation of 2D N = (2,2) SQCD with Exact Lattice Supersymmetry

Sugino¹,

Kikukawa²

2010

AIP Conference Proceedings

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In this paper, we introduce the overlap Dirac operator, which satisfies the Ginsparg-Wilson relation, to the matter sector of two-dimensional N = (2, 2) lattice supersymmetric QCD (SQCD) with preserving one of the supercharges. It realizes the exact chiral flavor symmetry on the lattice, to make possible to define the lattice action for general number of the flavors of fundamental and anti-fundamental matter multiplets and for general twisted masses. Furthermore, superpotential terms can be introduced with exact holomorphic or anti-holomorphic structure on the lattice. We also consider the lattice formulation of matter multiplets charged only under the central U(1) (the overall U(1)) of the gauge group G = U(N ), and then construct lattice models for gauged linear sigma models with exactly preserving one supercharge and their chiral flavor symmetry.

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“…where γ is a constant independent of the gauge fields, which takes the value γ = 1 32π 2 for the overlap Dirac operator [78], β µν (x) is a tensor field satisfying ∂ * µ β µν (x) = 0 which depends only on the SU(2) gauge field and k µ (x) is a local, gauge-invariant current which can be constructed so that it transforms as the axial vector current under the lattice symmetries. Moreover, taking into account the pseudo-scalar nature of q (1) L (x) under the charge conjugation and the pseudo reality of SU (2), one has…”

Section: Cancellations Of Sumentioning

confidence: 99%

A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance

Kikukawa¹

2009

Proceedings of the XXVI International Symposium on Lattice Field Theory — PoS(LATTICE 2008)

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We present a gauge-invariant and non-perturbative construction of the Glashow-Weinberg-Salam model on the lattice, based on the lattice Dirac operator satisfying the Ginsparg-Wilson relation. Our construction covers all SU(2) topological sectors with vanishing U(1) magnetic flux and would be usable for a description of the baryon number non-conservation. In infinite volume, it provides a gauge-invariant regularization of the electroweak theory to all orders of perturbation theory. First we formulate the reconstruction theorem which asserts that if there exists a set of local currents satisfying cetain properties, it is possible to reconstruct the fermion measure which depends smoothly on the gauge fields and fulfills the fundamental requirements such as locality, gauge-invariance and lattice symmetries. Then we give a closed formula of the local currents required for the reconstruction theorem.

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Weak coupling expansion of massless QCD with a Ginsparg-Wilson fermion and axial U(1) anomaly

Cited by 127 publications

References 30 publications

Aspects of chiral symmetry and the lattice

Aspects of chiral symmetry and the lattice

Ginsparg-Wilson Formulation of 2D N = (2,2) SQCD with Exact Lattice Supersymmetry

A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance

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