Mass Spectra of N=2 Supersymmetric SU(n) Chern-Simons-Higgs Theories

TL;DR

This paper develops an algebraic method to determine the mass spectra and symmetry breaking patterns in N=2 supersymmetric SU(n) Chern-Simons-Higgs theories, facilitating further studies in related quantum field theories.

Contribution

It introduces a natural basis for fields in these theories and relates the spectra to angular momentum addition, generalizable to other Lie groups.

Findings

Mass spectra are derived using algebraic methods.

Symmetry breaking patterns follow SU(2) algebra.

Method applicable to other classical Lie groups.

Abstract

An algebraic method is used to work out the mass spectra and symmetry breaking patterns of general vacuum states in N=2 supersymmetric SU(n) Chern-Simons-Higgs systems with the matter fields being in the adjoint representation. The approach provides with us a natural basis for fields, which will be useful for further studies in the self-dual solutions and quantum corrections. As the vacuum states satisfy the SU(2) algebra, it is not surprising to find that their spectra are closely related to that of angular momentum addition in quantum mechanics. The analysis can be easily generalized to other classical Lie groups.