Aspects of chiral symmetry and the lattice

Creutz, Michael

doi:10.1103/revmodphys.73.119

Cited by 106 publications

(118 citation statements)

References 116 publications

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“…Consequently it does not have spontaneous chiral symmetry breaking and hence no (pseudo-) Goldstone bosons and no easy definition of the quark mass [3]. In the lattice regularisation it is, however, possible to enhance the symmetry artificially by adding extra valence quarks which are quenched, that is, are not taken into account in the Boltzmann-weight of the gauge configurations by their fermion determinants.…”

Section: Partially Quenched Viewpointmentioning

confidence: 99%

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Hadron masses in QCD with one quark flavour

et al. 2007

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One-flavour QCD -a gauge theory with SU(3) colour gauge group and a fermion in the fundamental representation -is studied by Monte Carlo simulations. The mass spectrum of hadronic bound states is investigated in a volume with extensions of L ≃ 4.4 r 0 (≃ 2.2 fm) at two different lattice spacings: a ≃ 0.37 r 0 (≃ 0.19 fm) and a ≃ 0.27 r 0 (≃ 0.13 fm). The lattice action is Symanzik tree-level-improved Wilson action for the gauge field and (unimproved) Wilson action for the fermion.

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Section: Partially Quenched Viewpointmentioning

confidence: 99%

“…A dramatic consequence of the absence of (broken) chiral symmetry is the difficulty to find a unique definition of the point with zero quark mass in parameter space [3]. (For an excellent summary and discussion of this problem see [4].…”

Section: Introductionmentioning

confidence: 99%

Hadron masses in QCD with one quark flavour

et al. 2007

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“…Recent reviews discussing chiral symmetry on the lattice are found in Refs. [134,153,305,432,433,558].…”

Section: Fermions On the Latticementioning

confidence: 99%

θ dependence of SU(N) gauge theories in the presence of a topological term

2009

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We review results concerning the θ dependence of 4D SU (N ) gauge theories and QCD, where θ is the coefficient of the CP-violating topological term in the Lagrangian. In particular, we discuss θ dependence in the large-N limit.Most results have been obtained within the lattice formulation of the theory via numerical simulations. We review results at zero and finite temperature. We show that the results support the scenario obtained by general large-N scaling arguments, and in particular the Witten-Veneziano mechanism to explain the U (1) A problem. We also compare with results obtained by other approaches, especially in the large-N limit, where the issue has been also addressed using, for example, the AdS/CFT correspondence.We discuss issues related to theta dependence in full QCD: the neutron electric dipole moment, the dependence of the topological susceptibility on the quark masses, the U (1) A symmetry breaking at finite temperature.We also review results in the 2D CP N −1 model, which is an interesting theoretical laboratory to study issues related to topology.Finally, we discuss the main features of the two-point correlation function of the topological charge density.

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“…The lattice provides the primary non-perturbative method in field theory, but issues related to anomaly cancellation make that approach rather complicated. [21] Effective chiral Lagrangians provide another powerful route to non-perturbative information, although in a less quantitative manner due to increasing numbers of arbitrary parameters at higher order. To understand these issues better, the solvable models in two dimensions can provide insight into how chiral symmetry works.…”

Section: Four Dimensional Motivationsmentioning

confidence: 99%

Hidden symmetries in two dimensional field theory

Creutz¹

2006

Annals of Physics

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The bosonization process elegantly shows the equivalence of massless scalar and fermion fields in two space-time dimensions. However, with multiple fermions the technique often obscures global symmetries. Witten's non-Abelian bosonization makes these symmetries explicit, but at the expense of a somewhat complicated bosonic action. Frenkel and Kac have presented an intricate mathematical formalism relating the various approaches. Here I reduce these arguments to the simplest case of a single massless scalar field. In particular, using only elementary quantum field theory concepts, I expose a hidden SU (2) × SU (2) chiral symmetry in this trivial theory. I then discuss in what sense this field should be interpreted as a Goldstone boson.

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Aspects of chiral symmetry and the lattice

Cited by 106 publications

References 116 publications

Hadron masses in QCD with one quark flavour

Hadron masses in QCD with one quark flavour

θ dependence of SU(N) gauge theories in the presence of a topological term

Hidden symmetries in two dimensional field theory

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