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

TL;DR

This paper analyzes closed string dynamics in 2+1-dimensional space and SL(2,R) using Pohlmeyer reduction, identifying classes of string surfaces including spiky strings linked to singular Liouville fields and monodromy properties.

Contribution

It classifies string surfaces in $ r^{1,2}$ and $SL(2, r)$ based on fundamental quadratic forms, linking spiky strings to singular Liouville fields and their monodromy characteristics.

Findings

Identifies two classes of string surfaces in $ r^{1,2}$ and $SL(2, r)$.

Connects spiky strings to singular Liouville fields with specific monodromies.

Provides a framework for understanding conformal deformations of strings on Virasoro coadjoint orbits.

Abstract

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 $\pm I$. The first class in $SL(2,\rr)$ is parameterized by the Liouville fields with vanishing chiral energy functional. Similarly to $\rr^{1,2}$, the second class in $SL(2,\rr)$ describes spiky strings, related to the vacuum configurations of the $SL(2,\rr)/U(1)$ coset model.