On the origin of duality in the quantum Hall system

We discuss the possible origin of the duality observed in the quantum Hall current-voltage characteristics. We clarify the difference between "particle-vortex" (complex modular) duality, which acts on the full transport tensor, and "charge-flux" ("real") duality, which acts directly on the filling factor. Comparison with experiment strongly favors the form of duality which descends from the modular symmetry group acting holomorphically on the compexified conductivity.Comment: 5 pages, 3 figure

Experimental probes of emergent symmetries in the quantum Hall system

Experiments studying renormalization group flows in the quantum Hall system provide significant evidence for the existence of an emergent holomorphic modular symmetry $\Gamma_0(2)$. We briefly review this evidence and show that, for the lowest temperatures, the experimental determination of the position of the quantum critical points agrees to the parts \emph{per mille} level with the prediction from $\Gamma_0(2)$. We present evidence that experiments giving results that deviate substantially from the symmetry predictions are not cold enough to be in the quantum critical domain. We show how the modular symmetry extended by a non-holomorphic particle-hole duality leads to an extensive web of dualities related to those in plateau-insulator transitions, and we derive a formula relating dual pairs $(B,B_d)$ of magnetic field strengths across any transition. The experimental data obtained for the transition studied so far is in excellent agreement with the duality relations following from this emergent symmetry, and rule out the duality rule derived from the ``law of corresponding states". Comparing these generalized duality predictions with future experiments on other transitions should provide stringent tests of modular duality deep in the non-linear domain far from the quantum critical points.Comment: 12 pages, 9 figure

Spinor two-point functions in maximally symmetric spaces

The two-point function for spinors on maximally symmetric four-dimensional spaces is obtained in terms of intrinsic geometric objects. In the massless case, Weyl spinors in anti de Sitter space can not satisfy boundary conditions appropriate to the supersymmetric models. This is because these boundary conditions break chiral symmetry, which is proven by showing that the ldquoorder parameterrdquo $$\left\langle {\bar \psi \psi } \right\rangle$$ for a massless Dirac spinor is nonzero. We also give a coordinate-independent formula for the bispinor $$S(x)\bar S(x')$$ introduced by Breitenlohner and Freedman [1], and establish the precise connection between our results and those of Burges, Davis, Freedman and Gibbons [2]

One-Dimensional Flows in the Quantum Hall System

We construct the c-function whose gradient determines the RG flow of the conductivities (sigma_xy and sigma_xx) for a quantum Hall system, subject to two assumptions. (1) We take the flow to be invariant with respect to the infinite discrete symmetry group, recently proposed by several workers to explain the `superuniversality' of the delocalization exponents in these systems. (2) We also suppose the flow to be `quasi-holomorphic' (which we make precise) in the sense that it is as close as possible to a one-dimensional flow in the complex parameter sigma_xy +i sigma_xx. These assumptions together with the known asymptotic behaviour for large sigma_xx, completely determine the c-function, and so the phase diagram, for these systems. A complete description of the RG flow also requires a metric in addition to the c-function, and we identify the features which are required for this by the RG. A similar construction produces the c-function for other systems enjoying an infinite discrete symmetry, such as for supersymmetric QED.Comment: 17 pages of Te

New orbital solution for LS 5039 and search for period variability

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2023, Tutor: Marc Ribó GomisIn recent decades, the study of high-energy gamma-ray emitting astrophysical objects has led to the discovery of a new type of object called gamma-ray emitting binaries (GREB). Among the approximately 30 known GREBs, several consist of a compact object and a massive star. The ones characterised by having the peak of their spectral energy distribution at >∼ 1 MeV are called gamma-ray binaries (γBs). So far, ten γBs, including LS 5039, have been confirmed as sources of high and/or very high-energy γ-ray emission. Understanding the physical processes of binary systems like LS 5039 is crucial. As their behaviour depends on the orbital phase, obtaining comprehensive information about the orbital parameters and their potential evolution is of great importance. In this work, we report the study of the evolution of the orbital period of LS 5039 through the fitting of orbital solutions to radial velocities using the program Spectroscopy Binary Orbit Program (SBOP). Our study revealed no significant variation within the observed time frame. The new orbital solution we derived, Porb = 3.90599 ± 0.00002 day, is an order of magnitude more precise than the previous solution. Additionally, we assessed the potential impact of energy loss due to the emission of gravitational waves on the orbital period evolution, concluding that it was too small to significantly influence the result

Global quantum Hall phase diagram from visibility diagrams

We propose a construction of a global phase diagram for the quantum Hall effect. This global phase diagram is based on our previous constructions of visibility diagrams in the context of the Quantum Hall Effect. The topology of the phase diagram we obtain is in good agreement with experimental observations (when the spin effect can be neglected). This phase diagram does not show floating.Comment: LaTeX2e, 9 pages, 5 eps figure