Gravitational Cheshire effect from Yang-Mills instantons
Abstract
We show that the dimensional reduction of four-dimensional Yang-Mills instantons naturally gives rise to nontrivial matter configurations in three dimensions exhibiting an unusual mechanism of gravitational screening. Starting from Euclidean Yang-Mills theory, we reduce (anti-)self-dual gauge configurations along a compact direction generated by a U(1) isometry of the instanton background. Under this reduction, the gauge connection decomposes into a three-dimensional Yang-Mills field and an adjoint Higgs field, while the metric gives rise, as usual, to a dilaton and an Abelian gauge connection. For instantons on the Taub-NUT background, the reduced fields organize themselves into two mutually screening pairs: the backreaction of the Abelian sector cancels internally, and the same occurs independently in the non-Abelian sector. As a result, the full matter content supports a composite stealth configuration on flat three-dimensional space. By contrast, the dimensional reduction of instantons on the Eguchi-Hanson background yields a non-Abelian matter sector whose gravitational backreaction cancels, while the Abelian sector remains gravitationally active and therefore deforms the three-dimensional background geometry. These examples reveal a direct connection between four-dimensional (anti-)self-duality and three-dimensional BPS-type relations, and illustrate how instantonic sectors that are gravitationally invisible in four dimensions can descend into either fully composite stealth configurations or partially stealth matter configurations after dimensional reduction.
Related
- A genuinely non-Abelian plane-wave solution of the SU(2) Yang-Mills equations
- Background-equivariant BRST observables and i-particle propagators from an auxiliary quartet in SU(3) Yang-Mills
- Gravitational instantons from closed superstring field theory
- One-loop unifying relations between Yang-Mills theory and the nonlinear sigma model from Berends-Giele currents
- Ovcharenko-Podolsky Einstein-Maxwell gravitational instantons
BibTeX
@misc{diez2026gravitational,
title = {{Gravitational Cheshire effect from Yang-Mills instantons}},
author = {Borja Diez},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24127},
eprint = {2610.24127},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24127},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gravitational Cheshire effect from Yang-Mills instantons
AU - Borja Diez
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.24127
UR - https://arxiv.org/abs/2610.24127
AB - We show that the dimensional reduction of four-dimensional Yang-Mills instantons naturally gives rise to nontrivial matter configurations in three dimensions exhibiting an unusual mechanism of gravitational screening. Starting from Euclidean Yang-Mills theory, we reduce (anti-)self-dual gauge configurations along a compact direction generated by a U(1) isometry of the instanton background. Under this reduction, the gauge connection decomposes into a three-dimensional Yang-Mills field and an adjoint Higgs field, while the metric gives rise, as usual, to a dilaton and an Abelian gauge connection. For instantons on the Taub-NUT background, the reduced fields organize themselves into two mutually screening pairs: the backreaction of the Abelian sector cancels internally, and the same occurs independently in the non-Abelian sector. As a result, the full matter content supports a composite stealth configuration on flat three-dimensional space. By contrast, the dimensional reduction of instantons on the Eguchi-Hanson background yields a non-Abelian matter sector whose gravitational backreaction cancels, while the Abelian sector remains gravitationally active and therefore deforms the three-dimensional background geometry. These examples reveal a direct connection between four-dimensional (anti-)self-duality and three-dimensional BPS-type relations, and illustrate how instantonic sectors that are gravitationally invisible in four dimensions can descend into either fully composite stealth configurations or partially stealth matter configurations after dimensional reduction.
ER -