The Casimir effect in Gribov-Zwanziger theory
Abstract
We consider Yang-Mills theory with two infinite parallel plates, separated by a distance L, that are perfect magnetic conductors (PMC) or perfect electric conductors (PEC). Recently, it was shown that the Gribov copy problem persists in such a setting. We then study the Gribov-Zwanziger (GZ) action in the presence of those boundaries using functional integral methods. Lagrange multiplier fields allow one to lift the boundary conditions into the action, after which the boundary modifications to the gluon propagator can straightforwardly be determined. In the PEC case, we provide evidence that, even when translation invariance is (partially) broken, the usual horizon term in the GZ action still restricts the functional integral to the Gribov region. We compute the Casimir energy for GZ with PMC or PEC plates, both directly from the functional integral and from the energy-momentum tensor, obtaining consistent results. We compare our analytical results with recent lattice data, in both 4D and 3D. A priori, one might expect that the boundary-modified gluon propagator introduces new L-dependencies into the GZ gap equation. This would make the Gribov mass γ dynamically dependent on L, implying an interesting interplay with the Casimir energy. However, we show that no such dynamical L-dependence occurs within the current approximation.
Related
- On Quasiparticles within the Refined Gribov-Zwanziger Model
- Gauge-parameter cancellation and finite form factors in one-loop quark scattering in the refined Gribov-Zwanziger framework
- Center-twisted Gribov spectra and the finite-volume Gaussian response in the refined Gribov--Zwanziger framework
- Examples of Gribov copies in the presence of planar boundaries, and an emergent boundary gauge invariance in Yang-Mills theory
- Quantum corrections to the Casimir effect in a scalar Hořava-Lifshitz theory with rough plates at low temperature
BibTeX
@misc{dudal2026casimir,
title = {{The Casimir effect in Gribov-Zwanziger theory}},
author = {David Dudal and Philipe De Fabritiis and Sebbe Stouten and David Vercauteren},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11448},
eprint = {2609.11448},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11448},
}
RIS
TY - UNPB
TI - The Casimir effect in Gribov-Zwanziger theory
AU - David Dudal
AU - Philipe De Fabritiis
AU - Sebbe Stouten
AU - David Vercauteren
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11448
UR - https://arxiv.org/abs/2609.11448
AB - We consider Yang-Mills theory with two infinite parallel plates, separated by a distance L, that are perfect magnetic conductors (PMC) or perfect electric conductors (PEC). Recently, it was shown that the Gribov copy problem persists in such a setting. We then study the Gribov-Zwanziger (GZ) action in the presence of those boundaries using functional integral methods. Lagrange multiplier fields allow one to lift the boundary conditions into the action, after which the boundary modifications to the gluon propagator can straightforwardly be determined. In the PEC case, we provide evidence that, even when translation invariance is (partially) broken, the usual horizon term in the GZ action still restricts the functional integral to the Gribov region. We compute the Casimir energy for GZ with PMC or PEC plates, both directly from the functional integral and from the energy-momentum tensor, obtaining consistent results. We compare our analytical results with recent lattice data, in both 4D and 3D. A priori, one might expect that the boundary-modified gluon propagator introduces new L-dependencies into the GZ gap equation. This would make the Gribov mass γ dynamically dependent on L, implying an interesting interplay with the Casimir energy. However, we show that no such dynamical L-dependence occurs within the current approximation.
ER -