On the connection between Quantum Mechanics and the geometry of two-dimensional strings

TL;DR

This paper explores the geometric relationship between quantum mechanics and two-dimensional string theory, focusing on black-hole backgrounds and the role of area-preserving symmetries in phase space.

Contribution

It provides a geometric interpretation linking quantum mechanics consistency with the infinite gauged `W-hair' property of two-dimensional stringy black holes.

Findings

Black-hole backgrounds in 2D string theory exhibit area-preserving symmetries.

The infinite gauged `W-hair' ensures compatibility with quantum mechanics.

A geometric perspective explains the stability of these black holes.

Abstract

On the basis of an area-preserving symmetry in the phase space of a one-dimensional matrix model - believed to describe two-dimensional string theory in a black-hole background which also allows for space-time foam - we give a geometric interpretation of the fact that two-dimensional stringy black holes are consistent with conventional quantum mechanics due to the infinite gauged `W-hair' property that characterises them.