ADHmangel

ADHMangel is a fictional computational framework designed to implement the ADHM construction in four-dimensional gauge theory. It provides a toolkit for manipulating ADHM data, generating instanton solutions, and visualizing corresponding gauge fields. The name combines the ADHM construction with the notion of an angel to emphasize guidance through the structure of moduli spaces.

Originating in a scholarly speculative setting, ADHMangel was conceived by a collaborative group of theoretical physicists and computational mathematicians in the late 1990s and early 2000s. It was released as an open-source project with a modular architecture intended to support experimentation, reproducibility, and extension by researchers across subfields of gauge theory.

Key features include data structures for ADHM data (the matrices B1, B2, I, J), routines to impose the ADHM constraints, and algorithms to explore instanton moduli spaces. The framework offers a Python API with a high-level interface and a C++ backend for performance, numerical linear algebra utilities, solvers for consistency conditions, and basic visualization tools for gauge-field configurations. It is designed to be cross-platform and extensible.

Applications span theoretical physics education and research, enabling students and researchers to construct explicit instanton configurations, study moduli-space geometry, and test conjectures in a transparent, programmable environment. Because it emphasizes reproducibility, ADHMangel often includes example notebooks and validated datasets that illustrate common workflows in instanton theory.

Reception within the fictional community positions ADHMangel as a convenient reference implementation and teaching aid, with multiple forks and extensions exploring higher instanton numbers and alternative gauge groups. The project notes limitations, such as numerical sensitivity near singular points and the combinatorial growth of data with instanton number.