Phase structure of Higgs-Yukawa systems with chirally invariant lattice fermion actions

Tominaga, S.; Zenkin, Sergei V.

doi:10.1103/physrevd.50.3387

Cited by 6 publications

(16 citation statements)

References 33 publications

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“…Whether a system has the PMS phase can be examined within mean-field approximation. We consider the case of radially frozen Higgs field, Φ † n Φ n = 1, using the technique developed in [19]. For that, it is sufficient to consider the gauge interactions turned off.…”

Section: Phase Diagrammentioning

confidence: 99%

“…where dΦ is the Haar measure on the group, and Z f [yΦ] is the fermion partition function in the external field Φ. According to [19], the critical lines separating symmetric (paramagnetic) phases, where the vacuum expectation value of the Higgs field Φ = 0, from the broken (ferromagnetic) phases, where Φ = 0, are determined by the expression…”

Section: Phase Diagrammentioning

confidence: 99%

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Domain wall fermions with Majorana couplings

1997

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We examine the lattice boundary formulation of chiral fermions with either an explicit Majorana mass or a Higgs-Majorana coupling introduced on one of the boundaries. We demonstrate that the low-lying spectrum of the models with an explicit Majorana mass of the order of an inverse lattice spacing is chiral at tree level. Within a mean-field approximation we show that the systems with a strong Higgs-Majorana coupling have a symmetric phase, in which a Majorana mass of the order of an inverse lattice spacing is generated without spontaneous breaking of the gauge symmetry. We argue, however, that the models within such a phase have a chiral spectrum only in terms of the fermions that are singlets under the gauge group. The application of such systems to nonperturbative formulations of supersymmetric and chiral gauge theories is briefly discussed.

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Section: Phase Diagrammentioning

confidence: 99%

Section: Phase Diagrammentioning

confidence: 99%

Domain wall fermions with Majorana couplings

1997

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“…In Ref. [5] it is claimed that it is sufficient for this purpose to know F up to quadratic terms in h and h s . The following calculation of the derivatives of the phase transition lines at A will show, however, that quartic terms (or, in their absence, higher order terms) are indispensable; neglecting them leads to incorrect statements about a possible FI phase near A.…”

Section: Phase Structure At Amentioning

confidence: 99%

“…In a recent publication [5], mean-field calculations were presented for a general class of These discrepancies motivated us to carry out the present study, which may however have a wider applicability. We analyse the phase structure around the point A from a general point of view, in the mean-field approximation.…”

Section: Introductionmentioning

confidence: 99%

Ferrimagnetic phases in chiral Yukawa models

1995

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“…whose action although is non-local, is originated from the local mirror fermion action after integrating out the mirror fermions (see [3] and also [2]). In all the cases the fermions couple to the Higgs fields in the same way.…”

Section: The Action Of the Systemmentioning

confidence: 99%

Which Higgs-Yukawa systems can posses non-trivial fixed points

Zenkin

1995

Nuclear Physics B - Proceedings Supplements

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We argue that non-trivial fixed points bordering on the paramagnetic and ferromagnetic phases are most likely to exist in the Higgs-Yukawa systems that have a connected domain with the paramagnetic phase and no ferrimagnetic phase. We find three examples of such systems; among them is the U(1) system with naive fermions.1. In this talk we want to emphasize the following three points:(i) that the phase structure of the HiggsYukawa systems depend crucially both on on their symmetry group and on the form of the lattice fermion action, even though the coupling of the fermions to the Higgs fields is the same;(ii) that the most likely candidates for the systems with non-trivial fixed points bordering on the paramagnetic (PM) and ferromagnetic (FM) phases are the systems that have a connected domain with the PM phase and no ferrimagnetic (FI) phase;(iii) that one of such systems is the U(1) system with naive fermions.We investigate the phase diagrams of the Z 2 , U(1) and SU(2) Higgs-Yukawa systems with radially frozen Higgs fields for three types of chirally invariant lattice fermion actions. Our method is based on the variational mean field approximation, where contribution of the fermion determinant is calculated for weak and strong Yukawa coupling regimes in a certain ladder approximation [1,2]. The action of the systemhas two parameters: the scalar hopping parameter κ and the Yukawa coupling y; φ a are real components of the group-valued field Φ,Φ = P L Φ † + P R Φ. Given group, the system is determined by the form of the lattice Dirac operator D. At κ > 0 it corresponds to certain continuum Higgs-Yukawa model; at non-positive κ such a correspondence is distroyed. We shall require the system to be chirally invariant and operator D to have the form:We consider three examples of the lattice fermions satisfying these conditions: naive fermions withnon-local SLAC fermions withand fermions withwhose action although is non-local, is originated from the local mirror fermion action after integrating out the mirror fermions (see [3] and also [2]). In all the cases the fermions couple to the Higgs fields in the same way.3. The method [1,2] yields closed analytical expressions for the critical lines κ(y) between the FM and PM phases and between the antiferromagnetic (AM) and PM phases in the weak

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Phase structure of Higgs-Yukawa systems with chirally invariant lattice fermion actions

Cited by 6 publications

References 33 publications

Domain wall fermions with Majorana couplings

Domain wall fermions with Majorana couplings

Ferrimagnetic phases in chiral Yukawa models

Which Higgs-Yukawa systems can posses non-trivial fixed points

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