Dynamical mass reduction in the massive Yang-Mills spectrum in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>dimensions

Cubero, Axel Cortés; Orland, Peter

doi:10.1103/physrevd.89.085027

Cited by 7 publications

(12 citation statements)

References 30 publications

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“…There seems to be a crossover between the two phases, instead of a sharp phase transition. This appears at first sight contradictory to the results of [2]; however, what they found is that the crossover seems to disappear as the volume of the system is increased. Their calculations suggest that there is a Higgs phase, but it disappears as they move towards infinite volume.…”

Section: Introductioncontrasting

confidence: 75%

“…The author and P. Orland proposed studying the (1+1)-dimensional theory as a gauged principal chiral sigma model (PCSM) [2]. We found that in the continuum theory at infinite volume, there is only a confined phase.…”

Section: Introductionmentioning

confidence: 98%

“…Inspired by the nontrivial results of [3], we extend the approach started in [2] to study analytically the (1+1)-dimensional theory with a lattice discretization and at finite volume. Our analytic computation is so far only possible at large-N , so it cannot be directly compared to the N = 2 results of [3].…”

Section: Introductionmentioning

confidence: 99%

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Confinement-Higgs phase crossover as a lattice artifact in 1 + 1 dimensions

Cubero

2015

J. High Energ. Phys.

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We examine the phase structure of massive Yang-Mills theory in 1+1 dimensions. This theory is equivalent to a gauged principal chiral sigma model. It has been previously shown that the gauged theory has only a confined phase, and no Higgs phase in the continuum, and at infinite volume. There are no massive gluons, but only hadron-like bound states of sigma-model particles. The reason is that the gluon mass diverges, being proportional to the two-point correlation function of the renormalized field of the sigma model at x = 0. We use exact large-N results to show that after introducing a lattice regularization and typical values of the coupling constants used in Monte Carlo simulations, the gluon mass becomes finite, and even sometimes small. A smooth crossover into a Higgs phase can then appear. For small volumes and large N , we find an analytic expression for the gluon mass, which depends on the coupling constants and the volume. We argue that this Higgs phase is qualitatively similar to the one observed in lattice computations at N = 2.

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Section: Introductioncontrasting

confidence: 75%

Section: Introductionmentioning

confidence: 98%

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Confinement-Higgs phase crossover as a lattice artifact in 1 + 1 dimensions

Cubero

2015

J. High Energ. Phys.

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“…One can in principle find the bound-state spectrum by calculating the wave function and eigenvalues of (3.1). We have found this wave function for the meson-like bound states in the nonrelativistic limit, in Reference [9]. A relativistic approach for treating confinement in integrable field theories with nonintegrable deformations has been introduced in [10], which goes beyond the level of our analysis of this model.…”

Section: The Bound-state Spectrum In Massive Yang-millsmentioning

confidence: 99%

“…The Hamiltonian of massive Yang-Mills theory in the completely-fixed axial gauge, A 0 = 0, A 1 (t = 0) = 0, is found in detail in Ref. [9], to be…”

Section: The Bound-state Spectrum In Massive Yang-millsmentioning

confidence: 99%

The Hadronic Spectrum and Confined Phase in (1+1)-Dimensional Massive Yang-Mills Theory

Cubero

2015

Proceedings of the 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014)

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Massive Yang-Mills theory is known to be renormalizable in 1+1 dimensions. The gluon mass is introduced by coupling the gauge field to an SU(N) principal chiral nonlinear sigma model. The proof of renormalizability relies on the asymptotic freedom of the sigma model. However, renormalization forces the gluon mass to infinity. The continuum theory is in a confined phase rather than a Higgs phase. The physical excitations of the system are hadron-like bound states of sigma model particles. We calculate the massive spectrum of meson-like bound states analytically, using the exact S-matrix of the sigma model. The baryon-like spectrum can be found in principle by solving a quantum mechanical N-body problem. We remark on the evidence for the confined phase found for SU(2) in recent lattice simulations by Gongyo and Zwanziger. Their simulations show evidence for a Higgs-like phase which seems to disappear with increasing volume, finding agreement with our analysis in the continuum.

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

Gongyo

Zwanziger

2015

J. High Energ. Phys.

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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 FradkinShenker-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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Dynamical mass reduction in the massive Yang-Mills spectrum in1+1dimensions

Cited by 7 publications

References 30 publications

Confinement-Higgs phase crossover as a lattice artifact in 1 + 1 dimensions

Confinement-Higgs phase crossover as a lattice artifact in 1 + 1 dimensions

The Hadronic Spectrum and Confined Phase in (1+1)-Dimensional Massive Yang-Mills Theory

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

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