A Lorentzian Gribov no-pole condition is defined as the absence of source-free solutions to the Faddeev-Popov wave equation obeying the Feynman boundary condition, equivalent to injectivity of the negative-frequency ghost scattering map for localized backgrounds and a functional determinant restrict
An all-order proof of the equivalence between Gribov's no-pole and Zwanziger's horizon conditions
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abstract
The quantization of non-Abelian gauge theories is known to be plagued by Gribov copies. Typical examples are the copies related to zero modes of the Faddeev-Popov operator, which give rise to singularities in the ghost propagator. In this work we present an exact and compact expression for the ghost propagator as a function of external gauge fields, in SU(N) Yang-Mills theory in the Landau gauge. It is shown, to all orders, that the condition for the ghost propagator not to have a pole, the so-called Gribov's no-pole condition, can be implemented by demanding a nonvanishing expectation value for a functional of the gauge fields that turns out to be Zwanziger's horizon function. The action allowing to implement this condition is the Gribov-Zwanziger action. This establishes in a precise way the equivalence between Gribov's no-pole condition and Zwanziger's horizon condition.
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hep-th 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
In 3D Yang-Mills-Chern-Simons-Higgs theory the Gribov parameter fixed via gap equation reveals a confining phase with complex poles and a deconfined phase with physical gluon excitations.
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A Lorentzian Gribov no-pole condition for Yang-Mills theory
A Lorentzian Gribov no-pole condition is defined as the absence of source-free solutions to the Faddeev-Popov wave equation obeying the Feynman boundary condition, equivalent to injectivity of the negative-frequency ghost scattering map for localized backgrounds and a functional determinant restrict
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Charting the different phases of Yang-Mills-Chern-Simons-Higgs theories
In 3D Yang-Mills-Chern-Simons-Higgs theory the Gribov parameter fixed via gap equation reveals a confining phase with complex poles and a deconfined phase with physical gluon excitations.