Holography and (1+1)-dimension non-relativistic Quantum Mechanics

TL;DR

This paper extends the holographic duality concept to (1+1)-dimensional non-relativistic quantum systems, demonstrating their correspondence with classical gravity in higher dimensions through specific examples like free particles and harmonic oscillators.

Contribution

It generalizes the AdS/CFT duality to non-relativistic quantum mechanics in low dimensions, providing a new holographic framework for such systems.

Findings

Non-relativistic quantum systems can be derived from 3D classical gravity via holography.

Quantum paths in 2D correspond to classical gravity paths in 3D.

Explicit dual descriptions for free particles and harmonic oscillators are constructed.

Abstract

I generalize classical gravity/quantum gauge theory duality in AdS/CFT correspondence to (1+1)-dimensional non-relativistic quantum mechanical system. It is shown that (1+1)-dimensional non-relativistic quantum mechanical system can be reproduced from holographic projection of (2+1)-dimension classical gravity at semiclassical limit. In this explanation every quantum path in 2-dimension corresponds to a classical path of 3-dimension gravity under definite holographic projection. I consider free particle and harmonic oscillator as two examples and find their dual gravity description.