Singular Liouville fields and spiky strings in $\rr^{1,2}$ and $SL(2,\rr)$

Understand

The closed string dynamics in $\rr^{1,2}$ and $SL(2,\rr)$ is studied within the scheme of Pohlmeyer reduction.

• In both spaces two different classes of string surfaces are specified by the structure of the fundamental quadratic forms.
• The first class in $\rr^{1,2}$ is associated with the standard lightcone gauge strings and the second class describes spiky strings and their conformal deformations on the Virasoro coadjoint orbits.
• These orbits correspond to singular Liouville fields with the monodromy matrixes $\pm I$.