scholarly journals Complex poles, spectral function and reflection positivity violation of Yang-Mills theory

2020 ◽  
Author(s):  
Kei-Ichi Kondo ◽  
Yui Hayashi ◽  
Ryutaro Matsudo ◽  
Yutaro Suda ◽  
Masaki Watanabe
Keyword(s):  
Spectral Function ◽  
Reflection Positivity ◽  
Yang Mills

scholarly journals INFRARED-SUPPRESSED GLUON PROPAGATOR IN 4D YANG–MILLS THEORY IN A LANDAU-LIKE GAUGE

2007 ◽  
Vol 22 (32) ◽  
pp. 2429-2438 ◽  
Author(s):  
ATTILIO CUCCHIERI ◽  
AXEL MAAS ◽  
TEREZA MENDES
Keyword(s):  
Finite Volume ◽  
Gluon Propagator ◽  
Three Dimensional ◽  
Landau Gauge ◽  
Coulomb Gauge ◽  
Dimensional Case ◽  
Gauge Parameter ◽  
Reflection Positivity ◽  
Yang Mills ◽  
Transverse Gluon

The infrared behavior of the gluon propagator is directly related to confinement in QCD. Indeed, the Gribov–Zwanziger scenario of confinement predicts an infrared vanishing (transverse) gluon propagator in Landau-like gauges, implying violation of reflection positivity and gluon confinement. Finite-volume effects make it very difficult to observe (in the minimal Landau gauge) an infrared suppressed gluon propagator in lattice simulations of the four-dimensional case. Here we report results for the SU(2) gluon propagator in a gauge that interpolates between the minimal Landau gauge (for gauge parameter λ equal to 1) and the minimal Coulomb gauge (corresponding to λ = 0). For small values of λ we find that the spatially-transverse gluon propagator D tr (0, |p|), considered as a function of the spatial momenta |p|, is clearly infrared suppressed. This result is in agreement with the Gribov–Zwanziger scenario and with previous numerical results in the minimal Coulomb gauge. We also discuss the nature of the limit λ→0 (complete Coulomb gauge) and its relation to the standard Coulomb gauge (λ = 0). Our findings are corroborated by similar results in the three-dimensional case, where the infrared suppression is observed for all considered values of λ.

scholarly journals Complex poles and spectral function of Yang-Mills theory

2019 ◽  
Vol 99 (7) ◽  
Author(s):  
Yui Hayashi ◽  
Kei-Ichi Kondo
Keyword(s):  
Spectral Function ◽  
Yang Mills

scholarly journals Reflection positivity and complex analysis of the Yang–Mills theory from a viewpoint of gluon confinement

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
Kei-Ichi Kondo ◽  
Masaki Watanabe ◽  
Yui Hayashi ◽  
Ryutaro Matsudo ◽  
Yutaro Suda
Keyword(s):  
Complex Analysis ◽  
Gluon Propagator ◽  
Complex Structure ◽  
Landau Gauge ◽  
Complex Conjugate ◽  
Reflection Positivity ◽  
Scalar Model ◽  
Physical Point ◽  
Yang Mills ◽  
Euclidean Region

Abstract In order to understand the confining decoupling solution of the Yang–Mills theory in the Landau gauge, we consider the massive Yang–Mills model which is defined by just adding a gluon mass term to the Yang–Mills theory with the Lorentz-covariant gauge fixing term and the associated Faddeev–Popov ghost term. First of all, we show that massive Yang–Mills model is obtained as a gauge-fixed version of the gauge-invariantly extended theory which is identified with the gauge-scalar model with a single fixed-modulus scalar field in the fundamental representation of the gauge group. This equivalence is obtained through the gauge-independent description of the Brout–Englert–Higgs mechanism proposed recently by one of the authors. Then, we reconfirm that the Euclidean gluon and ghost propagators in the Landau gauge obtained by numerical simulations on the lattice are reproduced with good accuracy from the massive Yang–Mills model by taking into account one-loop quantum corrections. Moreover, we demonstrate in a numerical way that the Schwinger function calculated from the gluon propagator in the Euclidean region exhibits violation of the reflection positivity at the physical point of the parameters. In addition, we perform the analytic continuation of the gluon propagator from the Euclidean region to the complex momentum plane towards the Minkowski region. We give an analytical proof that the reflection positivity is violated for any choice of the parameters in the massive Yang–Mills model, due to the existence of a pair of complex conjugate poles and the negativity of the spectral function for the gluon propagator to one-loop order. The complex structure of the propagator enables us to explain why the gluon propagator in the Euclidean region is well described by the Gribov–Stingl form. We try to understand these results in light of the Fradkin–Shenker continuity between confinement-like and Higgs-like regions in a single confinement phase in the complementary gauge-scalar model.

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