In this dissertation we explore how some information theory quantities can be formulated holographycally and used to explore and characterize strongly interacting quantum field theories. In Chapter 1 we give a holographic formulation of the Quantum Information Metric, a quantity that measures the distance between two infinitesimally different quantum states. After giving the general prescription we illustrate its use in different examples and show how it reproduces the expected field theory results.
In Chapter 2 we explore another quantum information theory quantity that finds vast applications in holography: entanglement entropy. In particular we focus on the regularization of the entanglement entropy for holographic interface theories. The fact that globally well defined Fefferman-Graham coordinates are difficult to construct makes the regularization of the holographic theory challenging. We introduce a simple new cut-off procedure, which we call ``double cut-off" regularization.
While the spirit of the first two chapters is to develop tools that can be used in studying quantum field theories holographically, in Chapters 3 and 4 we switch gears and explore a concrete example of holographic duality: we study type IIB Supergravity duals to 5 dimensional super-conformal field theories. In Chapter 3 we look at a class of bulk solutions without monodromy. The solutions exhibit mild singularities, which could potentially complicate holographic applications. We use the relation of the entanglement entropy for a spherical entangling surface to the free energy of the field theory on the five sphere as a well-motivated benchmark to assess how problematic the singularities are. The holographic supergravity computations give well-defined results for both quantities and they satisfy the expected relations. This supports the interpretation of the solutions as holographic duals for 5d SCFTs and gives first quantitative indications for the nature of the dual SCFTs.
In chapter 4 we discuss bulk solutions that include punctures around which the supergravity fields have non-trivial SL(2,R) monodromy. We show that punctures with infinitesimal monodromy match a probe 7-brane analysis using $\kappa$-symmetry and we construct
families of solutions with fixed 5-brane charges and punctures with finite monodromy, corresponding to fully backreacted 7-branes. We compute the sphere partition functions of the dual 5d SCFTs and use the results to discuss concrete brane web interpretations of the supergravity solutions.