Related papers: Beyond Anyons
(2+1)D topological orders possess emergent symmetries given by a group $\text{Aut}(\mathcal{C})$, which consists of the braided tensor autoequivalences of the modular tensor category $\mathcal{C}$ that describes the anyons. In this paper we…
The book presents the wide range of topics in two-dimensional physics of quantum Hall systems, especially fractional quantum Hall states. It starts with the fundamental problems of quantum statistics in two dimensions and the corresponding…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
The usual extensions of supersymmetry require the existence of a complex structure and the formulation of the theory on K\"{a}hler manifolds. It is shown, that by relaxing the constraints on the algebra of supercharges we can get new…
This thesis is dedicated to the study of symmetries in reduced models of gravity, with some frozen degrees of freedom. We focus on the minisuperspace reduction whith a finite number of degrees of freedom. Minisuperspaces are treated as…
We present a general algebraic framework for gauging a 0-form compact, connected Lie group symmetry in (2+1)d topological phases. Starting from a symmetry fractionalization pattern of the Lie group $G$, we first extend $G$ to a larger…
In this work we have studied the singular behaviour of gravitational theories with non symmetric connections. For this purpose we introduce a new criteria for the appearance of singularities based on the existence of black/white hole…
The existence of the theory of `twisted cotangent bundles' (symplectic groupoids) allows to study classical mechanical systems which are generalized in the sense that their configurations form a Poisson manifold. It is natural to study from…
This thesis embarks on a comprehensive investigation of modified gravity theories and their implications on the properties of compact objects. Our primary objective is to shed light on the fundamental nature of gravity by exploring…
In a previous paper, we discussed simple examples like particle on a circle and molecules to argue that mixed states can arise from anomalous symmetries. This idea was applied to the breakdown (anomaly) of color SU(3) in the presence of…
The classic black hole mechanics and thermodynamics are formulated for stationary black holes with event horizons. Alternative theories of gravity of interest for cosmology contain a built-in time-dependent cosmological "constant" and black…
The present lectures contain an introduction to possible new physics beyond the Standard Model. Having in mind first of all accelerator experiments of the nearest future we concentrate on supersymmetry, a new symmetry that relates bosons…
Fundamental fields are a natural outcome in cosmology and particle physics and might therefore serve as a proxy for more complex interactions. The equivalence principle implies that all forms of matter gravitate, and one therefore expects…
The existence of black holes is a central prediction of general relativity and thus serves as a basic consistency test for modified theories of gravity. In spherical symmetry, only two classes of dynamic solutions are compatible with the…
Intrinsically topologically ordered phases can host anyons. Here, we take the view that entanglement between anyons can give rise to an emergent geometry resembling Anti-de Sitter (AdS) space. We analyze the entanglement structure of…
Black holes have often provided profound insights into the nature of gravity and the structure of space-time. The study of the mathematical properties of black objects is a major research theme of contemporary theoretical physics. This…
We propose a family of order parameters to detect the symmetry fractionalization class of anyons in 2D topological phases. This fractionalization class accounts for the projective, as opposed to linear, representations of the symmetry group…
In this talk I review various notions of generalised global symmetry: higher-form, higher-group, and non-invertible symmetry. All these notions have had profound impact on quantum field theory research in the last decade. I highlight…
We introduce topological magnetic field in two-dimensional flat space, which admits a solution of scalar monopole that describes the nontrivial topology. In the Chern-Simons gauge field theory of anyons, we interpret the anyons as the…
Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's…