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No smooth real instanton saddles in self-dual Yang-Mills on AdS4
Abstract
In the self-dual limit of Yang-Mills theory on Euclidean AdS4 studied by Heuveline, Ruzziconi, Sheta and Strominger, the boundary condition of the second-order action becomes vacuous, but the boundary equation of the first-order action is non-trivial. We show that, with this equation, the vacuum is the only saddle with a real gauge field when both fields are smooth up to the conformal boundary, for any compact gauge group. In particular, the self-dual solutions of Sarioglu and Tekin (2009) are not saddles; we also correct their charges, which omitted a surface term at the conformal boundary. Complex saddles and singular limits remain open.
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BibTeX
@misc{tekin2026smooth,
title = {{No smooth real instanton saddles in self-dual Yang-Mills on AdS$_4$}},
author = {Bayram Tekin},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02655},
eprint = {2611.02655},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02655},
}
RIS
TY - UNPB
TI - No smooth real instanton saddles in self-dual Yang-Mills on AdS_4
AU - Bayram Tekin
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02655
UR - https://arxiv.org/abs/2611.02655
AB - In the self-dual limit of Yang-Mills theory on Euclidean AdS_4 studied by Heuveline, Ruzziconi, Sheta and Strominger, the boundary condition of the second-order action becomes vacuous, but the boundary equation of the first-order action is non-trivial. We show that, with this equation, the vacuum is the only saddle with a real gauge field when both fields are smooth up to the conformal boundary, for any compact gauge group. In particular, the self-dual solutions of Sarioglu and Tekin (2009) are not saddles; we also correct their charges, which omitted a surface term at the conformal boundary. Complex saddles and singular limits remain open.
ER -