Semi-classical strings in $(2+1)-$dimensional backgrounds

TL;DR

This paper explores the connection between classical strings and their semi-classical quantum models in (2+1)-dimensional geometries, providing specific examples of quantum behaviors that define the underlying space-time structure.

Contribution

It introduces a method to derive semi-classical quantum models from classical string configurations in arbitrary (2+1)-dimensional backgrounds.

Findings

Quantum oscillations and free particles are used to characterize classical strings.

The approach links string dynamics to space-time geometry.

Examples demonstrate the unique determination of geometry from quantum models.

Abstract

This study analyzes the geometrical relationship between a classical string and its semi-classical quantum model. From an arbitrary $(2+1)-$dimensional geometry, a specific ansatz for a classical string is used to generate a semi-classical quantum model. In this framework, examples of quantum oscillations and quantum free particles are presented that uniquely determine a classical string and the space-time geometry where its motion takes place.