Chiral lattice gauge theories and the strong coupling dynamics of a Yukawa-Higgs model with Ginsparg-Wilson fermions

Giedt, Joel; Poppitz, Erich

doi:10.1088/1126-6708/2007/10/076

Cited by 39 publications

(108 citation statements)

References 58 publications

(129 reference statements)

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“…The lattice formulation of chiral gauge theories is an outstanding problem with no practical solution yet, despite much recent progress; for reviews, see [8]. While not our topic here, we note that the recent constructions of [9,10] have some attractive features (for an earlier proposal of similar flavor, see [11]). Most importantly, they may offer a way around the difficult and unsolved problem of the explicit nonperturbative construction of the fermion measure for general chiral lattice gauge theories.…”

Section: Motivation and Summarymentioning

confidence: 96%

“…Ref. [9] aims to achieve this by combining older ideas [12] to use non-gauge strong dynamics to decouple the mirror fermions in a vectorlike theory with the recently discovered exact lattice chirality of the Neuberger-Dirac operator.A concrete two-dimensional realization of the proposal [9] has the gauged XY-model as an essential part and was studied in various limits in [10]. Recently, [13] considered the perturbative spectrum of the models of [9] at nonzero gauge coupling.…”

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"Light From Chaos" in Two Dimensions

Poppitz

Shang

2008

Int. J. Mod. Phys. A

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We perform a Monte-Carlo study of the lattice two-dimensional gauged XY-model. Our results confirm the strong-coupling expansion arguments that for sufficiently small values of the spin-spin coupling the "gauge symmetry breaking" terms decouple and the long-distance physics is that of the unbroken pure gauge theory. We find no evidence for the existence, conjectured earlier, of massless states near a critical value of the spin-spin coupling. We comment on recent remarks in the literature on the use of gauged XY-models in proposed constructions of chiral lattice gauge theories. I. MOTIVATION AND SUMMARYThe gauged two-dimensional lattice XY-model has been studied for quite some time. Its simplicity allows for analytic studies via lattice dualities and strong-coupling expansions [1] as well as for numerical analysis, in either a Hamiltonian [2] or Euclidean (see, e.g., [3]) formulation. The model exhibits many phenomena found in more complicated higher-dimensional theories, notably the presence of both confining and Higgs phases [1,2,4,5].The motivation for this short study stems from our interest in using the gauged XY-model, as well as its nonabelian higher-dimensional analogues [4,6,7], in lattice constructions of chiral gauge theories. The lattice formulation of chiral gauge theories is an outstanding problem with no practical solution yet, despite much recent progress; for reviews, see [8]. While not our topic here, we note that the recent constructions of [9,10] have some attractive features (for an earlier proposal of similar flavor, see [11]). Most importantly, they may offer a way around the difficult and unsolved problem of the explicit nonperturbative construction of the fermion measure for general chiral lattice gauge theories. Ref. [9] aims to achieve this by combining older ideas [12] to use non-gauge strong dynamics to decouple the mirror fermions in a vectorlike theory with the recently discovered exact lattice chirality of the Neuberger-Dirac operator.A concrete two-dimensional realization of the proposal [9] has the gauged XY-model as an essential part and was studied in various limits in [10]. Recently, [13] considered the perturbative spectrum of the models of [9] at nonzero gauge coupling. It was claimed there that the gauge boson is always massive and, therefore, the construction of [9, 10] was argued to be irrelevant to the study of unbroken chiral gauge theories, on account of this fact alone.This brings us to the main topic of this paper. The arguments of [13] do not invoke either the fermions or the strong mirror dynamics (admittedly, complicated and not yet completely understood), but concern only the spectrum of the gauged XY-model, arguing that it only * Electronic address: poppitz@physics.utoronto.ca † Electronic address: ywshang@physics.utoronto.ca has a phase with a massive gauge boson. This conclusion contradicts strong-coupling expansion arguments for the decoupling of the "gauge-breaking" terms for small values of the spin-spin coupling. As these arguments have been made many time...

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Section: Motivation and Summarymentioning

confidence: 96%

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confidence: 99%

"Light From Chaos" in Two Dimensions

Poppitz

Shang

2008

Int. J. Mod. Phys. A

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“…The interest in lattice Higgs-Yukawa models has therefore recently been renewed [4][5][6][15][16][17][18][19][20].…”

Section: Jhep01(2011)143mentioning

confidence: 99%

Higgs boson mass bounds in the presence of a very heavy fourth quark generation

Gerhold

Jansen

Kallarackal

2011

J. High Energ. Phys.

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Abstract:We study the effect of a potential fourth quark generation on the upper and lower Higgs boson mass bounds. This investigation is based on the numerical evaluation of a chirally invariant lattice Higgs-Yukawa model emulating the same Higgs-fermion coupling structure as in the Higgs sector of the electroweak Standard Model. In particular, the considered model obeys a Ginsparg-Wilson version of the underlying SU(2) L × U(1) Y symmetry, being a global symmetry here due to the neglection of gauge fields in this model. We present our results on the modification of the upper and lower Higgs boson mass bounds induced by the presence of a hypothetical very heavy fourth quark doublet. Finally, we compare these findings to the standard scenario of three fermion generations.

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“…by rescaling the coupling constants λ, κ, y and the Higgs field ϕ according to 14) where the constant C has to obey the condition…”

Section: Jhep09(2007)041mentioning

confidence: 99%

The phase structure of a chirally invariant lattice Higgs-Yukawa model for small and for large values of the Yukawa coupling constant

Gerhold¹,

Jansen²

2007

J. High Energy Phys.

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We consider a chirally invariant lattice Higgs-Yukawa model based on the Neuberger overlap operator D (ov) . As a first step towards the eventual determination of Higgs mass bounds we study the phase diagram of the model analytically in the large N flimit. We present an expression for the effective potential at tree-level in the regime of small Yukawa and quartic coupling constants and determine the order of the phase transitions. In the case of strong Yukawa couplings the model effectively becomes an O(4)-symmetric nonlinear σ-model for all values of the quartic coupling constant. This leads to the existence of a symmetric phase also in the regime of large values of the Yukawa coupling constant. On finite and small lattices, however, strong finite volume effects prevent the expectation value of the Higgs field from vanishing thus obscuring the existence of the symmetric phase at strong Yukawa couplings.

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Chiral lattice gauge theories and the strong coupling dynamics of a Yukawa-Higgs model with Ginsparg-Wilson fermions

Cited by 39 publications

References 58 publications

"Light From Chaos" in Two Dimensions

"Light From Chaos" in Two Dimensions

Higgs boson mass bounds in the presence of a very heavy fourth quark generation

The phase structure of a chirally invariant lattice Higgs-Yukawa model for small and for large values of the Yukawa coupling constant

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