Related papers: Topological Aspects of Matters and Langlands Progr…
At low temperatures the phase diagram for the quantum Hall effect has a powerful symmetry arising from the Law of Corresponding States. This symmetry gives rise to an infinite order discrete group which is a generalisation of…
We discuss the possible topological order/topological quantum field theory of different quantum Hall systems. Given the value of the Hall conductivity, we constrain the global symmetry of the low-energy theory and its anomaly. Specifically,…
The Swampland Program aims to address the question, "when does an effective field theory model of quantum gravity have an ultraviolet complete embedding in string theory?", and can be regarded as a bottom-up approach to investigations of…
We provide a short overview of recent progress made in our understanding of the dark sector based on the Swampland program which in turn is rooted in lessons from string theory. We explain how the existence of one extra mesoscopic dimension…
The doubled formulation of string theory, which is T-duality covariant and enlarges spacetime with extra coordinates conjugate to winding number, is reformulated and its geometric and topological features examined. It is used to formulate…
We study theoretically the parallel quantum wires of the experiment by Auslaender et al. [Science 308, 88 (2005)] at low electron density. It is shown that a Hall effect as observed in two- or three-dimensional electron systems develops as…
We explain how the geometric Langlands program inspires some recent new prospectives of classical arithmetic Langlands program and leads to the solutions of some problems in arithmetic geometry.
We review and extend the vertex algebra framework linking gauge theory constructions and a quantum deformation of the Geometric Langlands Program. The relevant vertex algebras are associated to junctions of two boundary conditions in a 4d…
Supersymmetric black holes provide an excellent theoretical laboratory to test ideas about quantum gravity in general and black hole entropy in particular. When four-dimensional supergravity is interpreted as the low-energy approximation of…
It is shown that the Jain mapping between states of integer and fractional quantum Hall systems can be described dynamically as a perturbative renormalization of an effective Chern-Simons field theory. The effects of mirror duality…
Motivated by the observation of the fractional quantum Hall effect in graphene, we consider the effective field theory of relativistic quantum Hall states. We find that, beside the Chern-Simons term, the effective action also contains a…
In this Chapter, we give a brief review of the state of the art of theoretical and experimental studies of synthetic magnetic fields and quantum Hall effects in ultracold atomic gases. We focus on integer, spin, and fractional Hall effects,…
A phenomenon can hardly be found that accompanied physical paradigms and theoretical concepts in a more reflecting way than magnetism. From the beginnings of metaphysics and the first classical approaches to magnetic poles and streamlines…
Recently, mirror symmetry is derived as T-duality applied to gauge systems that flow to non-linear sigma models. We present some of its applications to study quantum geometry involving D-branes. In particular, we show that one can employ…
We present a diagrammatic decomposition of the transition pair correlation function for the uniform electron gas. We demonstrate explicitly that ring and ladder diagrams are dual counterparts that capture significant long- and short-ranged…
We study the relationship between bipartite entanglement, subsystem particle number and topology in a half-filled free fermion system. It is proposed that the spin-projected particle numbers can distinguish the quantum spin Hall state from…
We survey some algebraic geometric aspects of mirror symmetry and duality in string theory. Some applications of computer algebra to algebraic geometry and string theory are shortly reviewed.
The entanglement spectroscopy, initially introduced by Li and Haldane in the context of the fractional quantum Hall effects, has stimulated an extensive range of studies. The entanglement spectrum is the spectrum of the reduced density…
Geometric Langlands duality is usually formulated as a statement about Riemann surfaces, but it can be naturally understood as a consequence of electric-magnetic duality of four-dimensional gauge theory. This duality in turn is naturally…
These pedagogical lecture notes present a general introduction to most aspects of the integer and fractional quantum Hall effects. This is followed by an extensive discussion of quantum Hall ferromagnetism, both for spins in single-layer…