Advances in Theoretical and Mathematical Physics

Volume 21 (2017)

Number 2

Twisted index theory on orbifold symmetric products and the fractional quantum Hall effect

Pages: 451 – 501

DOI: https://dx.doi.org/10.4310/ATMP.2017.v21.n2.a3

Authors

Matilde Marcolli (Department of Mathematics, California Institute of Technology, Pasadena, Calif., U.S.A.)

Kyle Seipp (Department of Mathematics, California Institute of Technology, Pasadena, Calif., U.S.A.)

Abstract

We extend the noncommutative geometry model of the fractional quantum Hall effect, previously developed by Mathai and the first author, to orbifold symmetric products. It retains the same properties of quantization of the Hall conductance at integer multiples of the fractional Satake orbifold Euler characteristics. We show that it also allows for interesting composite fermions and anyon representations, and possibly for Laughlin type wave functions.

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Published 7 July 2017