Examples of Gribov copies in the presence of planar boundaries, and an emergent boundary gauge invariance in Yang-Mills theory
Abstract
First, we explicitly construct zero-modes of the Yang-Mills Faddeev-Popov operator in the presence of two parallel plates, with either perfect electric (PEC) or perfect magnetic (PMC) boundary conditions imposed. This establishes the existence of Gribov copies with finite action, and even finite L_2-norm, in Yang-Mills theory with non-trivial interfaces. We adapt Henyey's construction, although the boundary configuration imposes extra restrictions on the ansatz for the gauge field. Second, we discuss the phenomenon of an emergent boundary gauge invariance for PEC and PMC plates in Yang-Mills theory. This shall be important when applying the Gribov-Zwanziger procedure to parallel plate setups, of relevance for non-perturbatively studying the non-Abelian Casimir effect in the future.
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BibTeX
@misc{dudal2026examples,
title = {{Examples of Gribov copies in the presence of planar boundaries, and an emergent boundary gauge invariance in Yang-Mills theory}},
author = {David Dudal and Luigi Rosa and Sebbe Stouten},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30447},
eprint = {2608.30447},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30447},
}
RIS
TY - UNPB
TI - Examples of Gribov copies in the presence of planar boundaries, and an emergent boundary gauge invariance in Yang-Mills theory
AU - David Dudal
AU - Luigi Rosa
AU - Sebbe Stouten
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30447
UR - https://arxiv.org/abs/2608.30447
AB - First, we explicitly construct zero-modes of the Yang-Mills Faddeev-Popov operator in the presence of two parallel plates, with either perfect electric (PEC) or perfect magnetic (PMC) boundary conditions imposed. This establishes the existence of Gribov copies with finite action, and even finite L_2-norm, in Yang-Mills theory with non-trivial interfaces. We adapt Henyey's construction, although the boundary configuration imposes extra restrictions on the ansatz for the gauge field. Second, we discuss the phenomenon of an emergent boundary gauge invariance for PEC and PMC plates in Yang-Mills theory. This shall be important when applying the Gribov-Zwanziger procedure to parallel plate setups, of relevance for non-perturbatively studying the non-Abelian Casimir effect in the future.
ER -