  We investigate existence of replica off-diagonal solutions in the
field-theoretical description of Sachdev-Ye-Kitaev model. To this end we
evaluate a set of local and non-local dynamic correlation functions in the long
time limit. We argue that the structure of the soft-mode Schwarzian action is
qualitatively different in replica-diagonal vs. replica-off-diagonal scenarios,
leading to distinct long-time predictions for the correlation functions. We
then evaluate the corresponding correlation functions numerically and compare
the simulations with analytical predictions of replica-diagonal and
replica-off-diagonal calculations. We conclude that all our numerical results
are in a quantitative agreement with the theory based on the replica-diagonal
saddle point plus Schwarzian and massive Gaussian fluctuations (the latter do
contain replica off-diagonal components). This seems to exclude any
contributions from replica-off-diagonal saddle points, at least on the time
scales shorter than the inverse many-body level spacing.
