Related papers: Topological defects, fractals and the structure of…
We provide a lightning review of the construction of (generalised) orbifolds [arXiv:0909.5013, arXiv:1210.6363] of two-dimensional quantum field theories in terms of topological defects, along the lines of [arXiv:1307.3141]. This universal…
We formulate a relation between quantum-mechanical coherent states and complex-differentiable structures on the classical phase space ${\cal C}$ of a finite number of degrees of freedom. Locally-defined coherent states parametrised by the…
We revisit the possibility of constructing non-invertible topological defects for the axial symmetry of massless QED, despite its ABJ anomaly. Dressing the defects with a topological quantum field theory with mixed $U(1)$ and…
Looking for a quantum-mechanical implementation of duality, we formulate a relation between coherent states and complex-differentiable structures on classical phase space ${\cal C}$. A necessary and sufficient condition for the existence of…
Topology forms a cornerstone in modern condensed matter and statistical physics, offering a new framework to classify the phases and phase transitions beyond the traditional Landau paradigm. However, it is widely believed that topological…
Topological defects are thought to be left behind by the cosmological phase transitions which occur as the universe expands and cools. Similar processes can be studied in the phase transitions which take place in the laboratory:…
Fractal geometries, characterized by self-similar patterns and non-integer dimensions, provide an intriguing platform for exploring topological phases of matter. In this work, we introduce a theoretical framework that leverages isospectral…
We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1$ $$ < $$ $$h$$ $$ <$$ $$ 2$, a fractal distribution…
The potential role of cosmic topological defects has raised interest in the astrophysical community for many years now. In this set of notes, we give an introduction to the subject of cosmic topological defects and some of their possible…
Perturbative estimates suggest that extended topological defects such as cosmic strings emit few particles, but numerical simulations of the fields from which they are constructed suggest the opposite. In this paper we study the decay of…
The topic of this letter is structure formation with topological defects. We first present a partially new, fully local and gauge invariant system of perturbation equations to treat microwave background and dark matter fluctuations induced…
We provide a pedagogical overview of defect models of structure formation. We first introduce the concept of topological defect, and describe how to classify them. We then show how defects might be produced in phase transitions in the Early…
As put forward in [arXiv:1907.12339] topological quantum field theories can be projected using so-called projection defects. The projected theory and its correlation functions can be completely realized within the unprojected one. An…
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…
In these Lectures a method is described to analyze the effect of quantum fluctuations on topological defect backgrounds up to the one-loop level. The method is based on the spectral heat kernel/zeta function regularization procedure, and it…
We discuss the appearance of fractional topological phases on cyclic evolutions of entangled qudits. The original result reported in Phys. Rev. Lett. \textbf{106}, 240503 (2011) is detailed and extended to qudits of different dimensions.…
Defects are a ubiquitous feature of ordered media. They have certain universal features, independent of the underlying physical system, reflecting their topological origins. While the topological properties of defects are robust, they…
In the past year several constructions of non-invertible symmetries in Quantum Field Theory in $d\geq 3$ have appeared. In this paper we provide a unified perspective on these constructions. Central to this framework are so-called theta…
The essence of the famed long-range entanglement as revealed in topologically ordered state is the paradoxical coexistence of short-range correlation and nonlocal information that cannot be removed through constant-depth local quantum…