Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice

Kadoh, Daisuke; Kikukawa, Yoshio; Nakayama, Yoichi

doi:10.1088/1126-6708/2004/12/006

Cited by 12 publications

(22 citation statements)

References 52 publications

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“…Since Tr 1 = x tr 1 and tr 1 = 2 d/2 , Tr 1 is always an even positive integer 10. As a recent attempt towards an implementation of this construction in actual numerical simulations, see ref [34]…”

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confidence: 99%

Majorana and Majorana-Weyl fermions in lattice gauge theory

Inagaki

Suzuki

2004

J. High Energy Phys.

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In various dimensional euclidean lattice gauge theories, we examine a compatibility of the Majorana decomposition and the charge conjugation property of lattice Dirac operators. In 8n and 1 + 8n dimensions, we find a difficulty to decompose a classical lattice action of the Dirac fermion into a system of the Majorana fermion and thus to obtain a factrized form of the Dirac determinant. Similarly, in 2 + 8n dimensions, there is a difficulty to decompose a classical lattice action of the Weyl fermion into a system of the Majorana-Weyl fermion and thus to obtain a factrized form of the Weyl determinant. Prescriptions based on the overlap formalism do not remove these difficulties. We argue that these difficulties are reflections of the global gauge anomaly associated to the real Weyl fermion in 8n dimensions. For this reason (besides other well-known reasons), a lattice formulation of the N = 1 super Yang-Mills theory in these dimensions is expected to be extremely difficult to find.

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confidence: 99%

Majorana and Majorana-Weyl fermions in lattice gauge theory

Inagaki

Suzuki

2004

J. High Energy Phys.

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“…Such a representation has been formulated in the original cohomological analysis in [5] on the infinite lattice. As has been shown in our previous paper [10], it is also possible to formulate the periodic vector-potential representation for the admissible gauge fields on the finite lattice.…”

Section: Admissible U(1) Gauge Fields On a Finite Latticementioning

confidence: 89%

“…This is because the magnetic flux m µν is invariant with respect to a local variation of the link field. As shown in [10], it is possible to establish the one-to-one correspondence betweeñ U(x, µ) and periodic vector potentialsÃ µ (x) which satisfỹ…”

Section: Admissible U(1) Gauge Fields On a Finite Latticementioning

confidence: 93%

A practical construction of U(1) chiral lattice gauge theories

Kadoh¹,

Kikukawa²

2005

Proceedings of XXIIIrd International Symposium on Lattice Field Theory — PoS(LAT2005)

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“…See also [33] for the case of the finite volume lattice. 3 The lattice symmetries mean translations, rotations, reflections and charge conjugation.…”

Section: Jhep05(2008)095mentioning

confidence: 99%

Application of Novel Ultrasonic Cleaning Equipment That Uses the Waveguide Mode for the Single-Wafer Cleaning Process

Suzuki¹,

Imazeki²,

Han³

et al. 2011

Jpn. J. Appl. Phys.

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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. JHEP05(2008)095suggested by 't Hooft's anomaly matching condition [5] and so on. Unfortunately, very little is known so far about the actual behavior of chiral gauge theories beyond perturbation theory. It is desirable to develop a formulation to study the non-perturbative aspect of chiral gauge theories.Despite the well-known problem of the species doubling [6 -9], lattice gauge theory can now provide a framework for non-perturbative formulation of chiral gauge theories. The clue to this development is the construction of local and gauge-covariant lattice Dirac operators satisfying the Ginsparg-Wilson relation [10 -15]. By this relation, it is possible to realize an exact chiral symmetry on the lattice [16], without the species doubling problem. It is also possible to introduce Weyl fermions on the lattice and this opens the possibility to formulate anomaly-free chiral lattice gauge theories [17 -29]. In the case of U(1) chiral gauge theories, Lüscher [18] proved rigorously that it is possible to construct the fermion path-integral measure which depends smoothly on the gauge field and fulfills the fundamental requirements such as locality, gauge-invariance and lattice symmetries. Although it is believed that a chiral gauge theory is a difficult case for numerical simulations because the effective action induced by Weyl fermions has a non-zero imaginary part, it would be still interesting and even useful to develop a formulation of chiral lattice gauge theories by which one can work out fermionic observables numerically as the functions of link field with exact gauge invariance. 1 In this article, we construct the SU(2) × U(1) chiral gauge theory of the Glashow-Weinberg-Salam model on the lattice, keeping the exact gauge invariance. As in the case of U(1) theories, we first formulate the reconstruction theorem which asserts that if there exists a set of local currents satisfying cetain properties, it is possible to reconstruct the chiral fermion measure which depends smoothly on the gauge field and fulfills the fundamental requirements such as locality, 2 gauge-invariance and lattice symmetries. 3 We then give a closed expr...

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Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice

Cited by 12 publications

References 52 publications

Majorana and Majorana-Weyl fermions in lattice gauge theory

Majorana and Majorana-Weyl fermions in lattice gauge theory

A practical construction of U(1) chiral lattice gauge theories

Application of Novel Ultrasonic Cleaning Equipment That Uses the Waveguide Mode for the Single-Wafer Cleaning Process

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