Speaker
Description
We discuss a controllable reduced sector of four-dimensional Euclidean Yang--Mills theory obtained from symmetric instantons through conformal equivalence and dimensional reduction. In this framework, circle-symmetric and spherically symmetric instantons give rise to hyperbolic magnetic monopoles on $H^3$ and hyperbolic vortices on $H^2$, providing a unified description of topological defects relevant to confinement. The reduced sector retains nontrivial confinement diagnostics: in a dilute semiclassical regime, ensembles of these defects yield area-law behavior of Wilson loops. We also emphasize a bulk-boundary viewpoint in which hyperbolic monopole data can be encoded by suitable boundary data. [arXiv: 2507.20372[hep-th]]
From the perspective of QuantHEP, this construction suggests a useful strategy for isolating lower-dimensional effective models that preserve key confinement observables while being more amenable to numerical treatment and, potentially, to quantum simulation or quantum-algorithmic implementation. We outline how hyperbolic reduced models may serve as benchmark settings for studying Wilson-loop observables, topological sectors, and boundary reconstruction in gauge theory.