  At zero temperature the negative-parity ground states of the nucleon and
delta baryons are non-degenerate with the positive-parity partners due to
spontaneous breaking of chiral symmetry. However, chiral symmetry is expected
to be restored at sufficiently high temperature, in particular when going from
the hadronic to the quark-gluon plasma (QGP) phase. This would imply that
channels with opposite parity become degenerate. We study the nucleon (spin
$1/2$) and $\Delta$ (spin $3/2$) baryons in both parity sectors using lattice
QCD. The range of temperatures spans both the hadronic and QGP phases. Using
the FASTSUM anisotropic $N_f = 2 + 1$ ensembles, we analyze the correlation
functions and the spectral functions using respectively exponential fits and
the Maximum Entropy Method. We find clear evidence of in-medium effects in the
hadronic phase, especially for the negative-parity ground state, and of parity
doubling in the QGP phase.
