Ghost condensation on the lattice

2005/08/31 by Attilio Cucchieri, Tereza Mendes, Antonio Mihara · 17 citations
Mathematics · Physics and Astronomy · #Combinatorics #Gauge theory #High-Energy Particle Collisions Research #Ising model #Lattice (music) #Lattice QCD #Lattice gauge theory #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Propagator #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Square lattice #hep-lat #hep-th #nucl-th

paper · pdf · doi:10.1103/physrevd.72.094505

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 72(9) (American Physical Society) · 16 pages, 8 figures and 3 tables; minor modifications in the text, figures and references

arxiv created 2005/11/02 · openalex publication_date 2005/11/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We perform a numerical study of ghost condensation---in the so-called Overhauser channel---for SU(2) lattice gauge theory in minimal Landau gauge. The off-diagonal components of the momentum-space ghost propagator G^cd(p) are evaluated for lattice volumes V=8⁴, 12⁴, 16⁴, 20⁴, 24⁴ and for three values of the lattice coupling: \ensuremathβ=2.2, 2.3, 2.4. Our data show that the quantity \ensuremathφ^b(p)=ϵ^bcdG^cd(p)/2 is zero within error bars, being characterized by very large statistical fluctuations. On the contrary, |\ensuremathφ^b(p)| has relatively small error bars and behaves at small momenta as L^\ensuremath-2p^\ensuremath-z, where L is the lattice side in physical units and z\ensuremath≈4. We argue that the large fluctuations for \ensuremathφ^b(p) come from spontaneous breaking of a global symmetry and are associated with ghost condensation. It may thus be necessary (in numerical simulations at finite volume) to consider |\ensuremathφ^b(p)| instead of \ensuremathφ^b(p), to avoid a null average due to tunneling between different broken vacua. Also, we show that \ensuremathφ^b(p) is proportional to the Fourier-transformed gluon field components \stackrel\texttildelowA_\ensuremathμ^b(q). This explains the L^\ensuremath-2 dependence of |\ensuremathφ^b(p)|, as induced by the behavior of |\stackrel\texttildelowA_\ensuremathμ^b(q)|. We fit our data for |\ensuremathφ^b(p)| to the theoretical prediction (r/L²+v)/(p⁴+v²), obtaining for the ghost condensate v an upper bound of about 0.058 GeV². In order to check if v is nonzero in the continuum limit, one probably needs numerical simulations at much larger physical volumes than the ones we consider. As a by-product of our analysis, we perform a careful study of the color structure of the inverse Faddeev-Popov matrix in momentum space.

Citations

• Consistent power corrections to ultraviolet asymptotic solutions in Yang–Mills theory
• On ghost condensation, mass generation and Abelian dominance in the maximal Abelian gauge
• Dynamical gluon mass generation from in linear covariant gauges
• Theory of Superconductivity
• Infrared features of the Landau gauge QCD
• Abelian dominance and gluon propagators in the maximally Abelian gauge of SU(2) lattice gauge theory
• Numerical study of the fundamental modular region in the minimal Landau gauge
• Microscopic Theory of Superconductivity
• Renormalization properties of the mass operator AμaAμa in three-dimensional Yang-Mills theories in the Landau gauge

Cited by

• Nonperturbative ghost dynamics in the maximal abelian gauge
• Study of the maximal Abelian gauge inSU(2)Euclidean Yang-Mills theory in the presence of the Gribov horizon