Topological phases of matter are ubiquitous in crystals, but less is known about their existence amorphous systems, that lack long-range order. In this perspective, we review the recent progress made on theoretically defining topological and new phenomenology they can open. We revisit key experiments suggesting exist both solid-state synthetic systems. finish by discussing open questions field,...

At its foundations, Maxwell’s theory of Electrodynamics, like thermodynamics, is a topological theory independent from geometric constraints of metric, scales, or gauge symmetries. One of the most interesting features of Electromagnetism is its relationship to the transport of momentum and energy by means of photons. This article utilizes a topological perspective to discuss the classical featu...

Topological Yang-Mills theory with the Belavin-Polyakov-Schwarz-Tyupkin SU (2) instanton is solved completely, revealing an underlying multi-link intersection theory. Link invariants are also shown to survive the coupling to a certain kind of matter (hyperinstantons). The physical relevance of topological field theory and its invariants is discovered. By embedding topological Yang-Mills theory ...

Keeping in mind the several models of M(atrix) theory we attempt to understand the possible structure of the topological M(atrix) theory “underlying” these approaches. In particular we are motivated by the issue about the nature of the structure of the vacuum of the topological M(atrix) theory and how this could be related to the vacuum of the electroweak theory. In doing so we are led to a sim...

Perturbing usual type B topological matter with vector (0, 1)-forms we find a topological theory which contains explicitly Kodaira-Spencer deformation theory. It is shown that, in genus zero, three-point correlation functions give the Yukawa couplings for a generic point in the moduli space of complex structures. This generalization of type B topological matter seems to be the correct framework...