  The origin of the low-lying nature of the $N$*(1440), or Roper resonance, has
been the subject of significant interest for many years, including several
investigations using lattice QCD. The majority of lattice studies have not
observed a low-lying excited state energy level in the region of the Roper
resonance. However, it has been claimed that chiral symmetry could play an
important role in our understanding of this resonance. The purpose of this
study is to systematically examine the role of chiral symmetry in the low-lying
nucleon spectrum by directly comparing the clover and overlap fermion actions.
To ensure any differences in results are attributable to the choice of fermion
action, simulations are performed on the same set of gauge field configurations
at matched pion masses. Correlation matrix techniques are employed to determine
the excitation energy of the first positive-parity excited state for each
action. The clover and overlap actions show a remarkable level of agreement. We
do not find any evidence that fermion action chiral symmetry plays a
significant role in understanding the Roper resonance on the lattice.
