Exploring the AdS/CFT Correspondence: Non-Relativistic Generalisations & Holographic Multiboundary Wormholes

Abstract

In this thesis I explore two pertinent avenues of the correspondence: the rich, pragmatic context of non-relatavistic holography and the story of holographic multiboundary wormholes and their relation to the profound interplay between bulk geometry and boundary entanglement.
In chapter , I introduce the correspondence and review the key ideas that motivate and underlie the work in subsequent chapters.
In chapter we consider the development of a holographic dictionary for asymptotically locally Schrdinger spacetimes for in a massive vector model in various spatial dimensions. We carry out a linearised analysis of bulk perturbations and identify the boundary data as sources and vevs for the dual stress-energy complex. We verify that a sensible asymptotic expansion of bulk perturbations in sub-leading powers of exists by expanding them in eigenvalues of the boundary dilatation operator.
The third chapter extends the work of the Chapter to the case with in the massive vector model, in various dimensions, where the additional lightlike direction is regarded as internal from the boundary point of view, qualitatively unlike the case.
Chapter considers the entanglement structure of states holographically dual to multiboundary wormholes in the high-temperature limit, in which the thermal scale associated to each boundary is much larger than the scale. We find that the entanglement structure in this limit is almost entirely bipartite in this regime.
The fifth chapter investigates the extent to which the results of chapter generalise to regions of small moduli. We utilise heuristic tensor network methods to construct tensor network models of multiboundary wormhole states built by sewing tensors to Coxeter tilings and their quotients. We find in several cases that we can construct holographic states representing multiboundary wormhole geometries for which the entanglement structure is mostly, or almost entirely bipartite.