Chern-Simons terms in noncommutative geometry and its application to bilayer quantum hall systems

Abstract

Considering bilayer systems as extensions of the planar ones by an internal space of two discrete points, we use the ideas of Noncommutative Geometry to construct the gauge theories for these systems. After integrating over the discrete space we find an effective 2 + 1 action involving an extra complex scalar field, which can be interpreted as arising from the tunneling between the layers. The gauge fields are found in different phases corresponding to the different correlations due to the Coulomb interaction between the layers. In a particular * On leave from High Energy Division, Centre

Extra dimension of space-time exposed by anomalies at low energy

“…This discrete dimension is necessary to unify all the interactions and the Higgs field as components of the extended gravity. The discrete extra dimension has also been shown to be relevant beyond the high-energy physics, in particular in the bilayer Quantum Hall systems [29]. Since the KK-siblings in DKKT is always a subset of the spectrum in the space-time with a continuous extra dimension, our result can be considered as the first test of the general idea of extra dimensions at low energy.…”

“…Last but not least, by these results we demon-strated that the extra dimension is not the exclusive task of the T eV and Planck scale physics. Its indication can be searched in nuclear physics as well as in condensed matter physics as suggested before [29].…”

Nonrelativistic Electron–electron Interaction in a Maxwell–chern–simons–proca Model Endowed With a Timelike Lorentz-Violating Background

“…This puts in evidence the relevance of nonusual mechanisms for the attainment of electron-electron attractiveness. It should also be mentioned that noncommutative Chern-Simons theories have been applied successfully to describe properties of planar Hall systems, [73][74][75][76][77][78] one of the points of clear connection of noncommutativity with condensed matter physics. The large number of applications of noncommutativity to condensed matter physics and the general relation between these mechanisms indicate that applications of Lorentz violation to condensed matter systems should be a sensible and feasible issue as well.…”