Phase structure and the gluon propagator of SU(2) gauge-Higgs model in two dimensions

Shinya Gongyo, Daniel Zwanziger

    Research output: Contribution to journalArticle

    Abstract

    Abstract: We study numerically the phase structure and the gluon propagator of the SU(2) gauge-Higgs model in two dimensions. First, we calculate gauge-invariant quantities, in particular the static potential from Wilson Loop, the W propagator, and the plaquette expectation value. Our results suggest that a confinement-like region and a Higgs-like region appear even in two dimensions. In the confinement-like region, the static potential rises linearly, with string breaking at large distances, while in the Higgs-like region, it is of Yukawa type, consistent with a Higgs-type mechanism. The correlation length obtained from the W propagator has a finite maximum between these regions. The plaquette expectation value shows a smooth cross-over consistent with the Fradkin-Shenker-Osterwalder-Seiler theorem. From these results, we suggest that there is no phase transition in two dimensions. We also calculate a gauge-dependent order parameter in Landau gauge. Unlike gauge invariant quantities, the gauge non-invariant order parameter has a line of discontinuity separating these two regions. Finally we calculate the gluon propagtor. We infer from its infrared behavior that the gluon propagator would vanish at zero momentum in the infinite-volume limit, consistent with an analytical study.

    Original languageEnglish (US)
    Article number2
    Pages (from-to)1-17
    Number of pages17
    JournalJournal of High Energy Physics
    Volume2015
    Issue number1
    DOIs
    StatePublished - 2015

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    propagation
    discontinuity
    strings
    theorems
    momentum

    Keywords

    • Gauge Symmetry
    • Higgs Physics
    • Lattice Gauge Field Theories
    • Spontaneous Symmetry Breaking

    ASJC Scopus subject areas

    • Nuclear and High Energy Physics

    Cite this

    Phase structure and the gluon propagator of SU(2) gauge-Higgs model in two dimensions. / Gongyo, Shinya; Zwanziger, Daniel.

    In: Journal of High Energy Physics, Vol. 2015, No. 1, 2, 2015, p. 1-17.

    Research output: Contribution to journalArticle

    Gongyo, Shinya ; Zwanziger, Daniel. / Phase structure and the gluon propagator of SU(2) gauge-Higgs model in two dimensions. In: Journal of High Energy Physics. 2015 ; Vol. 2015, No. 1. pp. 1-17.
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    N2 - Abstract: We study numerically the phase structure and the gluon propagator of the SU(2) gauge-Higgs model in two dimensions. First, we calculate gauge-invariant quantities, in particular the static potential from Wilson Loop, the W propagator, and the plaquette expectation value. Our results suggest that a confinement-like region and a Higgs-like region appear even in two dimensions. In the confinement-like region, the static potential rises linearly, with string breaking at large distances, while in the Higgs-like region, it is of Yukawa type, consistent with a Higgs-type mechanism. The correlation length obtained from the W propagator has a finite maximum between these regions. The plaquette expectation value shows a smooth cross-over consistent with the Fradkin-Shenker-Osterwalder-Seiler theorem. From these results, we suggest that there is no phase transition in two dimensions. We also calculate a gauge-dependent order parameter in Landau gauge. Unlike gauge invariant quantities, the gauge non-invariant order parameter has a line of discontinuity separating these two regions. Finally we calculate the gluon propagtor. We infer from its infrared behavior that the gluon propagator would vanish at zero momentum in the infinite-volume limit, consistent with an analytical study.

    AB - Abstract: We study numerically the phase structure and the gluon propagator of the SU(2) gauge-Higgs model in two dimensions. First, we calculate gauge-invariant quantities, in particular the static potential from Wilson Loop, the W propagator, and the plaquette expectation value. Our results suggest that a confinement-like region and a Higgs-like region appear even in two dimensions. In the confinement-like region, the static potential rises linearly, with string breaking at large distances, while in the Higgs-like region, it is of Yukawa type, consistent with a Higgs-type mechanism. The correlation length obtained from the W propagator has a finite maximum between these regions. The plaquette expectation value shows a smooth cross-over consistent with the Fradkin-Shenker-Osterwalder-Seiler theorem. From these results, we suggest that there is no phase transition in two dimensions. We also calculate a gauge-dependent order parameter in Landau gauge. Unlike gauge invariant quantities, the gauge non-invariant order parameter has a line of discontinuity separating these two regions. Finally we calculate the gluon propagtor. We infer from its infrared behavior that the gluon propagator would vanish at zero momentum in the infinite-volume limit, consistent with an analytical study.

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