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Jun 2, 2022

Jun 2, 2022

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Mar 25, 2024

Mar 25, 2024

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.

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open access

Scopus© citazioni

Data di acquisizione

Jun 2, 2022

Jun 2, 2022

Web of Science© citazioni

Data di acquisizione

Mar 25, 2024

Mar 25, 2024