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FQHE and tt * geometry

Bergamin, R.
•
Cecotti, S.
2019
  • journal article

Periodico
JOURNAL OF HIGH ENERGY PHYSICS
Abstract
Cumrun Vafa [1] has proposed a microscopic description of the Fractional Quantum Hall Effect (FQHE) in terms of a many-body Hamiltonian H invariant under four supersymmetries. The non-Abelian statistics of the defects (quasi-holes and quasi-particles) is then determined by the monodromy representation of the associated tt* geometry. In this paper we study the monodromy representation of the Vafa 4-susy model. Modulo some plausible assumption, we find that the monodromy representation factors through a Temperley-Lieb/Hecke algebra with q = ± exp (πi/ν) as predicted in [1]. The emerging picture agrees with the other predictions of [1] as well. The bulk of the paper is dedicated to the development of new concepts, ideas, and techniques in tt* geometry which are of independent interest. We present several examples of these geometric structures in various contexts.
DOI
10.1007/JHEP12(2019)172
WOS
WOS:000511696700001
SCOPUS
2-s2.0-85077307913
Archivio
http://hdl.handle.net/20.500.11767/111332
Diritti
open access
Soggetti
  • Anyons

  • Extended Supersymmetr...

  • Topological States of...

  • High Energy Physics -...

  • High Energy Physics -...

  • Physics - Mesoscopic ...

  • Mathematical Physics

  • Mathematics - Mathema...

  • Settore FIS/02 - Fisi...

Web of Science© citazioni
0
Data di acquisizione
May 31, 2022
Scopus© citazioni
0
Data di acquisizione
Jun 2, 2022
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