Global anomalies in chiral gauge theories on the lattice

Bär, Oliver; Plasencia, Isabel Campos

doi:10.1016/s0550-3213(00)00182-6

Cited by 27 publications

(42 citation statements)

References 20 publications

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“…However, there is another obstruction, namely Witten's global gauge anomaly [27]. 7 The presence of this obstruction in the SU(2) theory in the lattice setting has been demonstrated both numerically [6,8] and analytically (in the classical continuum limit) in [9]. This obstruction also has a natural description in the context of families index theory for the Dirac operator: There is a canonical trivialisation of the U(1) determinant line bundle over 1-dimensional balls (i.e.…”

Section: Relation To Gauge Anomalies In Lattice Chiral Gauge Theorymentioning

confidence: 99%

“…A lattice version of the index arose there as the fermionic topological charge of the lattice gauge field, and can be expressed as the index of the Overlap lattice Dirac operator, introduced in [5]. The fact that the overlap formulation successfully reproduces the global gauge anomaly and obstructions to the vanishing of local gauge anomalies [6,7,8,9,10] indicates that it should also lead to a lattice version of families index theory for the Dirac operator. The purpose of the present paper is to show that this is indeed the case.…”

Section: Introductionmentioning

confidence: 99%

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Families index theory for Overlap lattice Dirac operator. I

Adams¹

2002

Nuclear Physics B

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The index bundle of the Overlap lattice Dirac operator over the orbit space of lattice gauge fields is introduced and studied. Obstructions to the vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge theory have a natural description in this context. Our main result is a formula for the topological charge (integrated Chern character) of the index bundle over evendimensional spheres in the orbit space. It reduces under suitable conditions to the topological charge of the usual (continuum) index bundle in the classical continuum limit (this is announced and sketched here; the details will be given in a forthcoming paper). Thus we see that topology of the index bundle of the Dirac operator over the gauge field orbit space can be captured in a finitedimensional lattice setting.

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Section: Relation To Gauge Anomalies In Lattice Chiral Gauge Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Families index theory for Overlap lattice Dirac operator. I

Adams¹

2002

Nuclear Physics B

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“…This fact implies the cancellation of Witten's SU (2) anomaly (cf. [38,39]). Given the basis for the SU(2) doublets defined globally, one may try to extend the fermion measure to incorporate the U(1) gauge field following the reconstruction theorem [14].…”

Section: Electroweak Theorymentioning

confidence: 99%

Analytic progress on exact lattice chiral symmetry

Kikukawa

2002

Nuclear Physics B - Proceedings Supplements

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Theoretical issues of exact chiral symmetry on the lattice are discussed and related recent works are reviewed. For chiral theories, the construction with exact gauge invariance is reconsidered from the point of view of domain wall fermion. The issue in the construction of electroweak theory is also discussed. For vector-like theories, we discuss unitarity (positivity), Hamiltonian approach, and several generalizations of the Ginsparg-Wilson relation (algebraic and odd-dimensional).

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“…A local and gauge invariant current defines W only locally. In (12) it is pointed out that the current must take into account the global geometry of the bundle underlying the gauge field. Global anomalies arise when (12) is not satisfied.…”

Section: Fermionic Measuresmentioning

confidence: 99%

Global anomalies in Chiral Lattice Gauge Theory

BÃ¤r¹

2000

Nuclear Physics B - Proceedings Supplements

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As first realized by Witten an SU (2) gauge theory coupled to a single Weyl fermion suffers from a global anomaly. This problem is addressed here in the context of the recent developments on chiral gauge theories on the lattice. We find Witten's anomaly manifests in the impossibility of defining globally a fermion measure that reproduces the proper continuum limit. Moreover, following Witten's original argument, we check numerically the crossing of the lowest eigenvalues of Neuberger's operator along a path connecting two gauge fields that differ by a topologically non-trivial gauge transformation.

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Global anomalies in chiral gauge theories on the lattice

Cited by 27 publications

References 20 publications

Families index theory for Overlap lattice Dirac operator. I

Families index theory for Overlap lattice Dirac operator. I

Analytic progress on exact lattice chiral symmetry

Global anomalies in Chiral Lattice Gauge Theory

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