Classical solutions of $\lambda$-deformed coset models

TL;DR

This paper derives classical solutions for $ $-deformed coset models based on $SL(2, eal)/U(1)$ and $SU(2)/U(1)$, revealing two classes of solutions with distinct mathematical forms and analyzing their physical properties.

Contribution

It introduces two new classes of classical solutions for $ $-deformed coset models using different coordinate systems, including elliptic function solutions.

Findings

Solutions expressed in hyperbolic, trigonometric, and elliptic functions.

Analysis of boundary conditions and physical properties.

Similarity between second class solutions and pendulum motion.

Abstract

We obtain classical solutions of $\l$-deformed $\s$-models based on $SL(2,\mathbb{R})/U(1)$ and $SU(2)/U(1)$ coset manifolds. Using two different sets of coordinates, we derive two distinct classes of solutions. The first class is expressed in terms of hyperbolic and trigonometric functions, whereas the second one in terms of elliptic functions. We analyze their properties along with the boundary conditions and discuss string systems that they describe. It turns out that there is an apparent similarity between the solutions of the second class and the motion of a pendulum.