This is a project in theoretical physics. Our goal is to understand the properties of low-dimensional quantum many-body systems in the framework of topological quantum field theories. We will in particular focus on the role of nonlinear and interacting gauge theories, and by doing so bridge the gap between condensed matter physics, particle physics, and gravity. We will do this with two physical platforms in mind, namely, ultracold quantum gases and photonic lattices. Both these platforms offer unique possibilities to study phenomena across a broad range of physical scenarios and provide a deeper understanding of the interplay between topology and gauge theories, closely linked to experimental realisations. By doing so we will address fundamental questions about Nature, ranging from microscopic descriptions of quantum matter to aspects of quantum gravity. The back-action principle is key in this respect. Prominent examples are electromagnetism and gravity where matter tells space how to curve, and space tells matter how to move.