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 .These classical string energies will be reproduced in a dual one-loop gauge theory computation in Section 4.
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