Towards Weyl fermions on the lattice without artefacts

Hasenfratz, P.; Allmen, Reto von

doi:10.1088/1126-6708/2008/02/079

Cited by 17 publications

(28 citation statements)

References 33 publications

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“…Note that the above remarks refer to the continuum CP transformation: recently ref. 61 argued that in the trivial topological sector it is possible to define a lattice-modified version of CP, (which, like the modified chiral symmetry, reduces to the usual continuum CP-transform), under which the chiral action (26) (and measure) is invariant; see also 62,63 .…”

Section: Problems With Ginsparg-wilson Fermions In Chiral Gauge Theoriesmentioning

confidence: 99%

Chiral Lattice Gauge Theories via Mirror–fermion Decoupling: A Mission (Im)possible?

Poppitz

Shang

2010

Int. J. Mod. Phys. A

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This is a review of the status and outstanding issues in attempts to construct chiral lattice gauge theories by decoupling the mirror fermions from a vectorlike theory. In the first half, we explain why studying nonperturbative chiral gauge dynamics may be of interest, enumerate the problems that a lattice formulation of chiral gauge theories must overcome, and briefly review our current knowledge. We then discuss the motivation and idea of mirror-fermion decoupling and illustrate the desired features of the decoupling dynamics by a simple solvable toy model. The role of exact chiral symmetries and matching of 't Hooft anomalies on the lattice is also explained. The second, more technical, half of the article is devoted to a discussion of the known and unknown features of mirror-decoupling dynamics formulated with Ginsparg-Wilson fermions. We end by pointing out possible directions for future studies.

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Section: Problems With Ginsparg-wilson Fermions In Chiral Gauge Theoriesmentioning

confidence: 99%

Chiral Lattice Gauge Theories via Mirror–fermion Decoupling: A Mission (Im)possible?

Poppitz

Shang

2010

Int. J. Mod. Phys. A

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“…While this could still be controlled using extrapolations, the second problem cannot be circumvented. The lattice regularization introduces a gauge anomaly in the weak interactions, as it is incompatible with parity violation [18]. This problem is unresolved despite many efforts [19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Testing the mechanism of lepton compositeness

et al. 2021

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Strict gauge invariance requires that physical left-handed leptons are actually bound states of the elementary left-handed lepton doublet and the Higgs field within the standard model. That they nonetheless behave almost like pure elementary particles is explained by the Fr"ohlich-Morchio-Strocchi mechanism. Using lattice gauge theory, we test and confirm this mechanism for fermions. Though, due to the current inaccessibility of non-Abelian gauged Weyl fermions on the lattice, a model which contains vectorial leptons but which obeys all other relevant symmetries has been simulated.

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“…. 9 The precise definition of "all possible continuous paths" is unimportant as long as, for each path contained within the sum, the path ordered integration over the gauge fields defined in equation (30) remains differentiable, starts and terminates at the required locations, and contains the shortest path between the two points. It could, for example, either be defined to be the paths bound within the hypercube around x or not.…”

Section: The Blockingmentioning

confidence: 99%

“…A possible solution to this problem, which uses a lattice redefinition of the Parity operator, a different approach to that presented here, was recently suggested in[29]; see also the attempts using the perfect action formalism in[30,31]. An older overview of chiral gauge theories on the lattice can be found in[32].…”

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confidence: 99%

A renormalisation group derivation of the overlap formulation

Cundy

2010

Nuclear Physics B

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Starting from the continuum Dirac operator, I construct a renormalisation group blocking which transforms the continuum action into a lattice action, and I specifically consider the Wilson and overlap formalisms. For Wilson fermions the inverse blocking is non-local and thus invalid. However, I proceed to demonstrate that it is possible to construct a valid, local, blocking which, though dependent on the lattice spacing, generates the lattice overlap fermion action from the continuum action. Using this renormalisation group blocking for overlap fermions, I derive the Ginsparg-Wilson equations and the lattice chiral symmetry. I suggest how the construction of a lattice chiral gauge theory could follow naturally from this approach.Comment: v4: 39 pages, some very minor change

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Towards Weyl fermions on the lattice without artefacts

Cited by 17 publications

References 33 publications

Chiral Lattice Gauge Theories via Mirror–fermion Decoupling: A Mission (Im)possible?

Chiral Lattice Gauge Theories via Mirror–fermion Decoupling: A Mission (Im)possible?

Testing the mechanism of lepton compositeness

A renormalisation group derivation of the overlap formulation

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