Multiple Chern-Simons Fields on a Torus

TL;DR

This paper investigates the vacuum structure and Hilbert space of multiple intertwined Chern-Simons gauge fields on a torus, revealing their complex relations and effective theory approximations.

Contribution

It provides a detailed analysis of the vacuum structure and Hilbert space for multiple Chern-Simons fields on a torus, highlighting their matrix statistics and effective theory correspondence.

Findings

Wilson line integrals relate to vacuum degeneracy

Total momenta and Hamiltonian commute only in physical Hilbert space

Effective theory with one gauge field approximates the multiple fields

Abstract

Intertwined multiple Chern-Simons gauge fields induce matrix statistics among particles. We analyse this theory on a torus, focusing on the vacuum structure and the Hilbert space. The theory can be mimicked, although not completely, by an effective theory with one Chern-Simons gauge field. The correspondence between the Wilson line integrals, vacuum degeneracy and wave functions for these two theories are discussed. Further, it is obtained in both of these cases that the two total momenta and Hamiltonian commute only in the physical Hilbert space.