Remarks on topological models and fractional statistics

TL;DR

This paper discusses topological models with fractional statistics, their applications to quantum Hall effects and high-temperature superconductivity, and explores models involving antisymmetric tensor fields and their dimensional reductions.

Contribution

It reviews recent models of fractional spin with Pauli terms, BF theories in four dimensions, and their dimensional reductions, highlighting new approaches to fractional statistics and string interactions.

Findings

Fractional statistics are crucial for understanding quantum Hall effects.

Dimensional reduction yields new topological theories involving 2-forms and scalar fields.

Antisymmetric tensor fields may mediate string interactions in higher dimensions.

Abstract

One of the most intriguing aspects of Chern-Simons-type topological models is the fractional statistics of point particles which has been shown essential for our understanding of the fractional quantum Hall effects. Furthermore these ideas are applied to the study of high Tc superconductivity. We present here an recently proposed model for fractional spin with the Pauli term. On the other hand, in D=4 space-time, a Schwarz-type topological gauge theory with antisymmetric tensor gauge field, namely BF model, is reviewed. Antisymmetric tensor fields are conjectured as mediator of string interaction. A dimensional reduction of the previous model provides a (2+1) dimensional topological theory, which involves a 2-form B and a 0-form $\phi$. Some recent results on this model are reported. Recently, there have been thoughts of generalizing unusual statistics to extended objects in others space-time dimensions, and in particular to the case of strings in four dimensions. In this context, discussions about fractional spin and antisymmetric tensor field are presented.