Constructing Dualities from Quantum State Manifolds

TL;DR

This paper presents a systematic method to derive semi-classical gravitational duals from quantum state manifolds, connecting simple quantum systems to concepts in gauge/gravity duality and extending existing $AdS_2/CFT_1$ results.

Contribution

It introduces a new procedure for constructing gravitational duals from quantum states, providing explicit dictionaries for low and higher-dimensional cases.

Findings

Established a link between quantum state manifolds and $AdS_2/CFT_1$ duality.

Extended the duality framework to higher dimensions with explicit dictionaries.

Highlighted the need for additional bulk coordinates in higher-dimensional duals.

Abstract

The thesis develops a systematic procedure to construct semi-classical gravitational duals from quantum state manifolds. Though the systems investigated are simple quantum mechanical systems without gauge symmetry many familiar concepts from the conventional gauge/gravity duality come about in a very natural way. The investigation of the low-dimensional manifolds link existing results in the $AdS_2/CFT_1$ literature. We are able to extend these in various ways and provide an explicit dictionary. The higher dimensional investigation is also concluded with a simple dictionary, but this dictionary requires the inclusion of many bulk coordinates. Consequently further work is needed to relate these results to existing literature. Possible ways to achieve this are discussed.