A renormalisation group derivation of the overlap formulation

Cundy, Nigel

doi:10.1016/j.nuclphysb.2009.08.016

Cited by 7 publications

(33 citation statements)

References 46 publications

(82 reference statements)

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“…The notation of this section follows [3]. We have a partition function (for simplicity, we neglect the Yang-Mills term).…”

Section: Ginsparg-wilson Mappings and Chiral Symmetriesmentioning

confidence: 99%

“…As D 1 and D 0 are in the same Hilbert space, a mapping rather than blocking or averaging procedure is required to construct D 1 from D 0 , and there is no obvious reason to suppose that there is not some suitable choice of D 1 which allows invertible mappings. One possibility is explored in [3]. The construction of the chiral symmetry, chiral condensate, and currents then proceeds as outlined above.…”

Section: Application To the Lattice Overlap Operatormentioning

confidence: 99%

See 1 more Smart Citation

Gell Mann Oakes Renner relation for multiple chiral symmetries.

Cundy¹,

Lee²

2012

Proceedings of XXIX International Symposium on Lattice Field Theory — PoS(Lattice 2011)

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As a first step towards establishing a chiral perturbation theory for overlap fermions, we investigate whether there are any ambiguities in the expression for the pion mass resulting from multiple chiral symmetries. The concern is that, calculating the conserved current for Ginsparg Wilson chiral symmetries in the usual way, different expressions of the chiral symmetries lead to different currents. This implies an ambiguity in the definition of the pion and pion decay constant for all Ginsparg-Wilson expressions of the Dirac operator, including the overlap operator. We use a renormalisation group mapping procedure to consider local chiral symmetry transformations for a continuum Ginsparg-Wilson "Dirac-operator." We find that this naturally leads to an expression for the conserved current that differs from the standard expression by cut-off artefacts, but is independent of which of the Ginsparg-Wilson symmetries is chosen. We recover the standard expressions for the massive Dirac operator, propagator, and chiral condensate. With this in place, we proceed to calculate the pion mass in the mapped theory as a function of the quark mass, and discover a unique expression for F π and m π , recovering the usual Gell-Mann-Oakes-Renner relation, baring the substitution of the chiral condensate with its modified value. We hypothesise that the argument can be carried directly over to the lattice theory.

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“…The notation of this section follows [3]. We have a partition function (for simplicity, we neglect the Yang-Mills term).…”

Section: Ginsparg-wilson Mappings and Chiral Symmetriesmentioning

confidence: 99%

Section: Application To the Lattice Overlap Operatormentioning

confidence: 99%

Gell Mann Oakes Renner relation for multiple chiral symmetries.

Cundy¹,

Lee²

2012

Proceedings of XXIX International Symposium on Lattice Field Theory — PoS(Lattice 2011)

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“…one could use Schur's procedure, although my own work uses a different and more convenient decomposition), and then giving the off-lattice section an infinite mass in the continuum limit so that it leaves all physics unaffected and can be safely neglected in a numerical simulation. This procedure will, of course, not work for any arbitrary lattice Dirac operator -even if the Dirac operators are of the same rank, that does not necessarily or usually imply that the blockings are finite and invertible, but it does work for overlap fermions [7], as strongly implied by the observation that overlap fermions do, in fact, satisfy the Ginsparg-Wilson equation with local γ L and γ R .…”

Section: )mentioning

confidence: 99%

“…as a function which commutes with γ 5 and maps the eigenvectors of D 0 onto the eigenvectors of D[7], one obtains the family of chiral symmetries,…”

mentioning

confidence: 99%

A Ginsparg Wilson renormalisation group approach to lattice CP symmetry

Cundy¹

2011

Proceedings of the XXVIII International Symposium on Lattice Field Theory — PoS(Lattice 2010)

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There is a long standing challenge in lattice QCD concerning the relationship between C Psymmetry and lattice chiral symmetry: naïvely the chiral symmetry transformations are not invariant under C P. With results similar to a recent work by Igarashi and Pawlowski, I show that this is because charge conjugation symmetry has been incorrectly realised on the lattice. The naive approach, to directly use the continuum charge conjugation relations on the lattice, fails because the renormalisation group blockings required to construct a doubler free lattice theory from the continuum are not invariant under charge conjugation. Correctly taking into account the transformation of these blockings leads to a modified lattice C P symmetry for the fermion fields, which, for gauge field configurations with trivial topology, has a smooth limit to continuum C P as the lattice spacing tends to zero. After constructing C P transformations for one particular group of lattice chiral symmetries, I construct a lattice chiral gauge theory which is C P invariant and whose measure is invariant under gauge transformations and C P.

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“…In [4], I explored the possibility that the lattice overlap Dirac operator is connected to the continuum by a block renormalisation group transformation; this was motivated by consideration of their obedience to the renormalisation group derived Ginsparg-Wilson relation. The construction contained within that paper was incomplete, because it did not address how to construct the Yang-Mills action in a similar way.…”

Section: Introductionmentioning

confidence: 99%

Multigrid HMC algorithm for Ginsparg-Wilson fermions

Cundy¹

2010

Proceedings of the XXVII International Symposium on Lattice Field Theory — PoS(LAT2009)

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I describe a method that places the fermion fields and the gauge fields on different lattice spacings during the Hybrid Monte Carlo generation of Ginsparg-Wilson dynamical ensembles. The idea is motivated by Wilson's formulation of the renormalisation group. After outlining the underlying theory, I describe a method to perform most of the work of the HMC on a coarse lattice, only requiring to convert to and from the fine lattice once for each independent configuration. Because the bulk of the work takes place on the coarse lattice, including the calculation of most observables, this method saves over an order of magnitude in computer time over previous methods. The XXVII International Symposium on Lattice Field Theory

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A renormalisation group derivation of the overlap formulation

Cited by 7 publications

References 46 publications

Gell Mann Oakes Renner relation for multiple chiral symmetries.

Gell Mann Oakes Renner relation for multiple chiral symmetries.

A Ginsparg Wilson renormalisation group approach to lattice CP symmetry

Multigrid HMC algorithm for Ginsparg-Wilson fermions

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