The SL(2,R)WZWN string model as a deformed oscillator and its classical-quantum string regimes

TL;DR

This paper analyzes the SL(2,R) WZWN string model in AdS_3 space, revealing a deformed oscillator structure that exhibits a duality between quantum and classical regimes, with significant implications for string spectrum and uncertainty relations.

Contribution

It introduces a deformed oscillator framework for the SL(2,R) string model and demonstrates a natural classical-quantum duality without assumptions.

Findings

Highly excited strings are more quantum and more excited than non-deformed models.

The mass spectrum drastically changes between low and high excitation regimes.

A modified uncertainty relation appears in the quantum (high curvature) regime.

Abstract

We study the SL(2,R) WZWN string model describing bosonic string theory in AdS_3 space-time as a deformed oscillator together with its mass spectrum and the string modified SL(2,R) uncertainty relation. The SL(2,R) string oscillator is far more quantum (with higher quantum uncertainty) and more excited than the non deformed one. This is accompassed by the highly excited string mass spectrum which is drastically changed with respect to the low excited one. The highly excited quantum string regime and the low excited semiclassical regime of the SL(2,R) string model are described and shown to be the quantum-classical dual of each other in the precise sense of the usual classical-quantum duality. This classical-quantum realization is not assumed nor conjectured. The quantum regime (high curvature) displays a modified Heisenberg's uncertainty relation, while the classical (low curvature) regime has the usual quantum mechanics uncertainty principle.