Topological susceptibility at zero and finite T in SU(3) Yang-Mills theory

Allés, B.; D’Elia, Massimo; Giacomo, A. Di

doi:10.1016/s0550-3213(97)00205-8

Cited by 182 publications

(246 citation statements)

References 30 publications

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“…This indicates that the levels that cross zero to the left of the peak are not physically relevant consistent with the result that ρ(0; m) goes to zero in the continuum limit. The numbers for the topological susceptibility obtained in this manner are consistent with the results obtained by field theoretic methods [8]. The modes that cross zero to the left of the peak in ρ(0; m) correspond to small modes [6,3] and this is consistent with Fig.…”

Section: Discussionsupporting

confidence: 89%

Spectrum of the Hermitian Wilson Dirac operator

Narayanan

1999

Nuclear Physics B - Proceedings Supplements

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Section: Discussionsupporting

confidence: 89%

Spectrum of the Hermitian Wilson Dirac operator

Narayanan

1999

Nuclear Physics B - Proceedings Supplements

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“…In this case one has to consider the following quadratic Lagrangian, which can be obtained substituting the exponential expressions (5.4) of the fields U and X into Eq. (4.1): 11) where c ≡ c 1…”

Section: Radiative Decays Of the Pseudoscalar Mesonsmentioning

confidence: 99%

“…We have tried to see if this transition has (or has not) anything to do with the usual SU(L) ⊗ SU(L) chiral transition: various possible scenarios have been discussed in Section 2. In particular, supported by recent lattice results on the pure-YM topological susceptibility and the socalled "chiral susceptibilities" (which have been discussed at length in the Introduction), we have analysed a scenario in which a new U(1)-breaking condensate survives across * We use for the pure-YM topological susceptibility the value A = (180 ± 5 MeV) 4 , obtained from lattice simulations [36,37,11]. …”

mentioning

confidence: 94%

Reviewing the problem of the U(1) axial symmetry and the chiral transition in QCD

Marchi¹,

Meggiolaro²

2003

Nuclear Physics B

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We discuss the role of the U(1) axial symmetry for the phase structure of QCD at finite temperature. We expect that, above a certain critical temperature, also the U(1) axial symmetry will be (effectively) restored. We will try to see if this transition has (or has not) anything to do with the usual chiral transition: various possible scenarios are discussed. In particular, supported by recent lattice results, we analyse a scenario in which a U(1)-breaking condensate survives across the chiral transition. This scenario can be consistently reproduced using an effective Lagrangian model. The effects of the U(1) chiral condensate on the slope of the topological susceptibility in the full theory with quarks are studied: we find that this quantity (in the chiral limit of zero quark masses) acts as an order parameter for the U(1) axial symmetry above the chiral transition. Further information on the new U(1) chiral order parameter is derived from the study (at zero temperature) of the radiative decays of the "light" pseudoscalar mesons in two photons: a comparison of our results with the experimental data is performed. (PACS codes: 12.38.Aw, 12.39.Fe, 11.15.Pg, 11.30.Rd) IntroductionIt is generally believed that a phase transition which occurs in QCD at a finite temperature is the restoration of the spontaneously broken SU(L) ⊗ SU(L) chiral symmetry in association with L massless quarks. At zero temperature the chiral symmetry is broken spontaneously by the condensation of qq pairs and the L 2 − 1 J P = 0 − mesons are just the Goldstone bosons associated with this breaking [1]. At high temperatures the thermal energy breaks up the qq condensate, leading to the restoration of chiral symmetry. We expect that this property not only holds for massless quarks but also continues for a small mass region. The order parameter for the chiral symmetry breaking is apparently qq ≡ L i=1 q i q i : the chiral symmetry breaking corresponds to the non-vanishing of qq in the chiral limit sup(m i ) → 0. From lattice determinations of the chiral order parameter qq one knows that the SU(L) ⊗ SU(L) chiral phase transition temperature T ch , defined as the temperature at which the chiral condensate qq goes to zero (in the chiral limit sup(m i ) → 0), is nearly equal to the deconfining temperature T c (see, e.g., Ref. [2]). But this is not the whole story: QCD possesses not only an approximate SU(L) ⊗ SU(L) chiral symmetry, for L light quark flavours, but also a U(1) axial symmetry (at least at the classical level) [3,4]. The role of the U(1) symmetry for the finite temperature phase structure has been so far not well studied and it is still an open question of hadronic physics whether the fate of the U(1) chiral symmetry of QCD has or has not something to do with the fate of the SU(L) ⊗ SU(L) chiral symmetry.In the "Witten-Veneziano mechanism" [5,6] for the resolution of the U(1) problem, a fundamental role is played by the so-called "topological susceptibility" in a QCD without quarks, i.e., in a pure Yang-Mills (YM) theory, in...

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“…On the numerical side, the quenched topological susceptibility seems to settle down at a value χ q = (0.205 MeV) 4 with an estimated 10% error on χ q [78,76]. A specialty of the topological susceptibility is that its cut-off effects depend not only on the action but also on the details of the calculation (type and number of cooling steps) if non-chiral symmetric actions with a 'field theoretic' definition of ν are used.…”

Section: The Topological Susceptibilitymentioning

confidence: 99%