Vacuum Mass Spectra for SU(N) Self-Dual Chern-Simons-Higgs Systems

TL;DR

This paper analyzes the vacuum structure and excitation masses in SU(N) self-dual Chern-Simons-Higgs systems with adjoint matter, revealing a complex mass pattern linked to the number of partitions of N.

Contribution

It introduces a detailed study of the vacuum degeneracy and mass spectra in SU(N) self-dual Chern-Simons-Higgs models, highlighting the connection to partition theory.

Findings

Number of degenerate minima equals the number of partitions of N.

Mass spectra exhibit an intricate structure reflecting self-duality.

Vacuum configurations correspond to gauge inequivalent minima.

Abstract

We study the $SU(N)$ self-dual Chern-Simons-Higgs systems with adjoint matter coupling, and show that the sixth order self-dual potential has $p(N)$ gauge inequivalent degenerate minima, where $p(N)$ is the number of partitions of $N$. We compute the masses of the gauge and scalar excitations in these different vacua, revealing an intricate mass structure which reflects the self-dual nature of the model.