The quantum Hall effect on $ \mathbb{R}^{4}$

Henriette Elvang; Joseph Polchinski

doi:10.1016/S1631-0705(03)00038-0

Extra dimensions in physics and astrophysics/Dimensions supplémentaires/en physique et astrophysique

The quantum Hall effect on

ℝ^{4}

[L'effet Hall quantique sur

ℝ^{4}

]

Présenté par : Guy Laval

Henriette Elvang ¹ ; Joseph Polchinski ²

¹ Department of Physics, University of California, Santa Barbara, CA 93106, USA
² Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030, USA

Comptes Rendus. Physique, Volume 4 (2003) no. 3, pp. 405-417.

Résumé
Abstract

Zhang et Hu ont formulé un système de Hall quantique SU(2) sur la quatre-sphère, avec une dynamique de bord tridimensionnelle intéressante comprenant des états sans gap d'hélicité differente de zéro. Afin de comprendre la physique locale de leur modèle, nous étudions les systèmes de Hall quantique U(1) et SU(2) sur un $ℝ^{4}$ plat, avec pour bord un $ℝ^{3}$ plat. Dans le cas U(1) la dynamique de bord est essentiellement uni-dimensionnelle. La théorie SU(2) peut être formulée sur $ℝ^{4}$ pour n'importe quel isospin I, mais afin d'obtenir dans une théorie de bord plate nous devons prendre I→∞ comme Zhang et Hu. La théorie se simplifie dans cette limite, le bord devenant une collection de systèmes unidimensionnels. Nous discutons également des contraintes générales sur l'apparition de la gravité à partir de théories de champs non-gravitationnelles.

Zhang and Hu have formulated an SU(2) quantum Hall system on the four-sphere, with interesting three-dimensional boundary dynamics including gapless states of nonzero helicity. In order to understand the local physics of their model we study the U(1) and SU(2) quantum Hall systems on flat $ℝ^{4}$ , with flat boundary $ℝ^{3}$ . In the U(1) case the boundary dynamics is essentially one-dimensional. The SU(2) theory can be formulated on $ℝ^{4}$ for any isospin I, but in order to obtain a flat boundary theory we must take I→∞ as in Zhang and Hu. The theory simplifies in the limit, the boundary becoming a collection of one-dimensional systems. We also discuss general constraints on the emergence of gravity from nongravitational field theories.

Publié le : 2003-04-01

DOI : 10.1016/S1631-0705(03)00038-0

Affiliations des auteurs :

Henriette Elvang ¹ ; Joseph Polchinski ²

¹ Department of Physics, University of California, Santa Barbara, CA 93106, USA
² Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030, USA

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Henriette Elvang; Joseph Polchinski. The quantum Hall effect on $ \mathbb{R}^{4}$. Comptes Rendus. Physique, Volume 4 (2003) no. 3, pp. 405-417. doi : 10.1016/S1631-0705(03)00038-0. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/S1631-0705(03)00038-0/

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