Current algebra and exotic statistics in 6 dimensions

TL;DR

This paper explores how chiral fermions in six-dimensional space-time with SU(3) gauge fields exhibit exotic quantum statistics characterized by q-commutation relations with q being a nontrivial root of unity.

Contribution

It demonstrates the emergence of exotic statistics for localized solitons in 6D gauge theories, extending understanding of quantum algebra in higher dimensions.

Findings

Localized solitons obey q-commutation relations with q as a third root of unity

Chiral fermions in 6D gauge backgrounds exhibit nontrivial algebraic structures

Extension of current algebra concepts to higher-dimensional exotic statistics

Abstract

By studying ordinary chiral fermions in background gauge fields we show that in the case of gauge group SU(3) and space-time dimension 5+1 localized solitons obey $q-$ commutation relations with $q$ not equal to $\pm 1$ but a third root of unity.