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arXiv · 2611.02655

No smooth real instanton saddles in self-dual Yang-Mills on AdS$_4$

Bayram Tekin
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Abstract

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.

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Bayram Tekin. 2026-11-02. No smooth real instanton saddles in self-dual Yang-Mills on AdS$_4$. https://arxiv.org/abs/2611.02655

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