  After the detection of gravitational waves from compact binary coalescences,
the search for transient gravitational-wave signals with less well-defined
waveforms for which matched filtering is not well-suited is one of the
frontiers for gravitational-wave astronomy. Broadly classified into "short" $
\lesssim 1~$\,s and "long" $ \gtrsim 1~$\,s duration signals, these signals are
expected from a variety of astrophysical processes, including non-axisymmetric
deformations in magnetars or eccentric binary black hole coalescences. In this
work, we present a search for long-duration gravitational-wave transients from
Advanced LIGO and Advanced Virgo's third observing run from April 2019 to March
2020. For this search, we use minimal assumptions for the sky location, event
time, waveform morphology, and duration of the source. The search covers the
range of $2~\text{--}~ 500$~s in duration and a frequency band of $24 - 2048$
Hz. We find no significant triggers within this parameter space; we report
sensitivity limits on the signal strength of gravitational waves characterized
by the root-sum-square amplitude $h_{\mathrm{rss}}$ as a function of waveform
morphology. These $h_{\mathrm{rss}}$ limits improve upon the results from the
second observing run by an average factor of 1.8.
