Spectrum of two-dimensional $su(2)$ gauge theories coupled to massless fermions in integer representations

TL;DR

This paper numerically investigates the spectra of two-dimensional $su(2)$ gauge theories with massless fermions in integer representations, revealing the presence or absence of massless states and their properties across different representations.

Contribution

It provides new numerical results on the spectra of $su(2)$ gauge theories with integer fermion representations for $J=2,3,4$, including the discovery of massless modes for higher $J$ values.

Findings

No massless states for $J=2$, with the lightest state being a boson.

Exact massless modes found for $J=3$ and $J=4$ in all momentum sectors.

Massless modes increase with total momentum, indicating a rich spectrum.

Abstract

The spectra of two-dimensional $su(2)$ gauge theories coupled to a single massless Majorana fermion in integer representations, $J$, are numerically investigated using the Discrete Light-Cone Hamiltonian. One of our aims is to explore the possible presence of massless states for $J>2$ in spite of the absence of a continuous symmetry. After comparing to existing results for $J=1$ (adjoint fermions), we present results for $J=2,3,4$. As expected, for $J=2$ there are no massless states but in contrast to the $J=1$ theory, the lightest state is a boson. We find exact massless modes in the bosonic and fermionic sector for all values of total momentum for $J=3$ and $J=4$ and, in each sector, the number of massless modes grows with the value of the total momentum. In addition to the spectrum, we present results on the particle number and momentum fraction distributions and argue for a separation of bulk states from edge states.