Jonathan Delgado | Search arXiv

arXiv2026

Symplectic Yang-Mills Theory

On a symplectic manifold, any differential two-form has a natural decomposition into two components: a primitive part and a non-primitive one. Applying this decomposition to the curvature two-form of a principal bundle over a symplectic manifold, we obtain a natural splitting of the Yang-Mills (YM) functional into two functionals that intrinsically depend on the symplectic structure: the primitive Yang-Mills (PYM) functional and the trace Yang-Mills (TYM) functional. We work out the basic properties of the critical solutions of these two functionals. The PYM functional in particular exhibits many of the desirable properties of the YM functional, including the ellipticity of its Euler-Lagrange equations and an algebraic classification of its flat solutions on G-bundles. We also prove a monotonicity formula for the PYM functional as a first step towards characterizing its moduli space of solutions.

math.SG↗

arXiv2024

Machine- and deep-learning-driven angular momentum inference from BHEX observations of the $n=1$ photon ring

The $n=1$ photon ring is an important probe of black hole (BH) properties and will be resolved by the Black Hole Explorer (BHEX) for the first time. However, extraction of black hole parameters from observations of the $n=1$ subring is not trivial. Developing this capability can be achieved by building a sample of $n=1$ subring simulations, as well as by performing feature extraction on this high-volume sample to track changes in the geometry, which presents significant computational challenges. Here, we present a framework for the study of $n=1$ photon ring behavior and BH property measurement from BHEX images. We use KerrBAM to generate a grid of $\gtrsim10^6$ images of $n=1$ photon rings spanning the entire space of Kerr BH spins and inclinations. Intensity profiles are extracted from images using a novel feature extraction method developed specifically for BHEX. This novel method is highly optimized and outperforms existing EHT methods by a factor of ${\sim}3000$. Additionally, we propose a novel, minimal set of geometric measurables for characterizing the behavior of the $n=1$ subring geometry. We apply these measurables to our simulation grid and test spin recovery on simulated images using: (i) gradient boosting, a machine learning algorithm; and (ii) an extension of Deep Horizon, a deep learning framework. We find $\gtrsim90$\% correct recovery of BH properties using the machine/deep learning approaches, and characterize the space of resolution-dependent geometric degeneracies. Finally, we test both approaches on GRMHD simulations of black hole accretion flows, and report accurate recovery of spin at the expected inclination of M87*.

astro-ph.HE↗