### 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 language | English (US) |
---|---|

Article number | 2 |

Pages (from-to) | 1-17 |

Number of pages | 17 |

Journal | Journal of High Energy Physics |

Volume | 2015 |

Issue number | 1 |

DOIs | |

State | Published - 2015 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2015*(1), 1-17. [2]. https://doi.org/10.1007/JHEP01(2015)002

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

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2015, no. 1, 2, pp. 1-17. https://doi.org/10.1007/JHEP01(2015)002

}

TY - JOUR

T1 - Phase structure and the gluon propagator of SU(2) gauge-Higgs model in two dimensions

AU - Gongyo, Shinya

AU - Zwanziger, Daniel

PY - 2015

Y1 - 2015

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.

KW - Gauge Symmetry

KW - Higgs Physics

KW - Lattice Gauge Field Theories

KW - Spontaneous Symmetry Breaking

UR - http://www.scopus.com/inward/record.url?scp=84921373187&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84921373187&partnerID=8YFLogxK

U2 - 10.1007/JHEP01(2015)002

DO - 10.1007/JHEP01(2015)002

M3 - Article

VL - 2015

SP - 1

EP - 17

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 1

M1 - 2

ER -