Self-Dual Yang-Mills in AdS4
Abstract
Quantum Yang-Mills theory in Euclidean AdS4 with Neumann boundary conditions is studied as a function of the complex couplings 1/g±2 ≡ 1/g2∓ (i θ)/(8 π2). We define a "self-dual limit" by g- → 0 with g+ fixed. We argue that the limiting theory is well-defined perturbatively and equivalent to the BF formulation of self-dual Yang-Mills theory with a particular boundary condition relating B and F at the boundary ∂AdS4. g+ is the loop-counting parameter of the self-dual theory. This is in stark contrast to flat space, where θ has no effect on perturbative dynamics. In the self-dual limit, it is shown that all tree-level zero-plus and single-plus boundary correlators vanish. A closed form expression is given for any number of gluons for the double-plus tree correlators. Finally, we show that in the flat space limit of AdS4, the total energy poles in the tree boundary correlators correctly reduce to the single-minus gluon amplitudes.
Related
- No smooth real instanton saddles in self-dual Yang-Mills on AdS4
- Classical solitons in anti-self-dual Yang-Mills theory
- On equivalence between solution structures of the anti-self-dual Yang--Mills equations
- Realization of several related (2+1)-dimensional integrable systems via an anti-self-dual Yang--Mills reduction
- A genuinely non-Abelian plane-wave solution of the SU(2) Yang-Mills equations
BibTeX
@misc{heuveline2026selfdual,
title = {{Self-Dual Yang-Mills in AdS$_4$}},
author = {Simon Heuveline and Romain Ruzziconi and Ahmed Sheta and Andrew Strominger},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27731},
eprint = {2608.27731},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27731},
}
RIS
TY - UNPB
TI - Self-Dual Yang-Mills in AdS_4
AU - Simon Heuveline
AU - Romain Ruzziconi
AU - Ahmed Sheta
AU - Andrew Strominger
PY - 2026
DA - 2026/08/27
PB - arXiv
DO - 10.48550/arxiv.2608.27731
UR - https://arxiv.org/abs/2608.27731
AB - Quantum Yang-Mills theory in Euclidean AdS_4 with Neumann boundary conditions is studied as a function of the complex couplings 1/g_±^2 ≡ 1/g^2∓ (i θ)/(8 π^2). We define a "self-dual limit" by g_- → 0 with g_+ fixed. We argue that the limiting theory is well-defined perturbatively and equivalent to the BF formulation of self-dual Yang-Mills theory with a particular boundary condition relating B and F at the boundary ∂AdS_4. g_+ is the loop-counting parameter of the self-dual theory. This is in stark contrast to flat space, where θ has no effect on perturbative dynamics. In the self-dual limit, it is shown that all tree-level zero-plus and single-plus boundary correlators vanish. A closed form expression is given for any number of gluons for the double-plus tree correlators. Finally, we show that in the flat space limit of AdS_4, the total energy poles in the tree boundary correlators correctly reduce to the single-minus gluon amplitudes.
ER -