In Figure 3, we have plotted the energies of the folded and circular string solutions against the filling
fraction
. As expected from the “string pendulum” picture of (20
), the folded string solution has
lower energy for fixed filling fraction
: The pendulum does not perform a full turn, but oscillates back
and forth. Note that the folded string approaches
in the limit
, which is the rotating
point-particle solution of Section 2.1. The quantum fluctuations about it correspond to the
plane-wave string domain. Note also that the simplest circular string solution with
discussed in Section 3.1 is the minimum (
) of the full circular string solution for
.
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