A possible constructive approach to (super-φ3)4 (III). On the normalization of Schwinger functions

The construction of massless Majorana fermions with chiral Yukawa couplings on the lattice is considered. We find topological obstructions tightly linked to those underlying the Nielsen-Ninomiya no-go theorem. In contradistinction to chiral fermions the obstructions originate only from the combination of the Dirac action and the Yukawa term. These findings are used to construct a chirally invariant lattice action. We also show that the path integral of this theory is given by the Pfaffian of the corresponding Dirac operator. As an application of the approach set-up here we construct a CP-invariant lattice action of a chiral gauge theory, based on a lattice adaptation of charge conjugation and parity transformation in the continuum.

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“…The action (7) could also be obtained by a Majorana reduction, see e.g. [26,27]. Note that chiral invariance of (7) is trivial, because…”

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confidence: 99%

Majorana fermions and CP-invariance of chiral gauge theories on the lattice

Igarashi

Pawlowski

2009

Nuclear Physics B

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“…For four dimensional Euclidean space, we have B * B = −1 which leads to ψ * * = − ψ. Therefore, there are no Majorana spinors satisfying the reality constraint [17,18]. This difficulty can be circumvented by doubling the fermions and implementing a symplectic Majorana condition…”

Section: Majorana Fermions and Yukawa Couplingsmentioning

confidence: 99%

CP invariance of chiral gauge theories and Majorana-Yukawa couplings on the lattice

Igarashi

Pawlowski

2009

Preprint

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The construction of CP-invariant lattice chiral gauge theories and the construction of lattice Majorana fermions with chiral Yukawa couplings is subject to topological obstructions. In the present work we suggest lattice extensions of charge and parity transformation for Weyl fermions. This enables us to construct lattice chiral gauge theories that are CP invariant. For the construction of Majorana-Yukawa couplings, we discuss two models with symplectic Majorana fermions: a model with two symplectic doublets, and one with an auxiliary doublet.

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“…5 This Majorana reduction, in a level of the functional integral, corresponds to the prescription of ref. [33].…”

Section: Action and Its Symmetriesmentioning

confidence: 99%

Effect of Ambient Gases on Emission Properties of Pd-Ni-Si-Be-B LM Ion Source

Arimoto¹,

Miyauchi²,

Hashimoto³

1987

Jpn. J. Appl. Phys.

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A lattice Wess-Zumino model is formulated on the basis of Ginsparg-Wilson fermions. In perturbation theory, our formulation is equivalent to the formulation by Fujikawa and Ishibashi and by Fujikawa. Our formulation is, however, free from a singular nature of the latter formulation due to an additional auxiliary chiral supermultiplet on a lattice. The model posssesses an exact U(1) R symmetry as a supersymmetric counterpart of the Lüscher lattice chiral U(1) symmetry. A restration of the supersymmetric Ward-Takahashi identity in the continuum limit is analyzed in renormalized perturbation theory. In the one-loop level, a supersymmetric continuum limit is ensured by suitably adjusting a coefficient of a single local termF * F . The non-renormalization theorem holds to this order of perturbation theory. In higher orders, on the other hand, coefficents of local terms with dimension ≤ 4 that are consistent with the U(1) R symmetry have to be adjusted for a supersymmetric continuum limit. The origin of this complexicity in higher-order loops is clarified on the basis of the Reisz power counting theorem. Therefore, from a view point of supersymmetry, the present formulation is not quite better than a lattice Wess-Zumino model formulated by using Wilson fermions, although a number of coefficients which require adjustment is much less due to the exact U(1) R symmetry. We also comment on an exact non-linear fermionic symmetry which corresponds to the one studied by Bonini and Feo; an existence of this exact symmetry itself does not imply a restoration of supersymmetry in the continuum limit without any adjustment of parameters.

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A possible constructive approach to (super-φ3)4 (III). On the normalization of Schwinger functions

Cited by 20 publications

References 14 publications

Majorana fermions and CP-invariance of chiral gauge theories on the lattice

Majorana fermions and CP-invariance of chiral gauge theories on the lattice

CP invariance of chiral gauge theories and Majorana-Yukawa couplings on the lattice

Effect of Ambient Gases on Emission Properties of Pd-Ni-Si-Be-B LM Ion Source

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