Precisietests van de AdS/CFT-correspondentie

The AdS/CFT correspondence, or holographic duality, relates quantum field theories with quantum gravity in one dimension higher. In this thesis, we study precision holography in various examples, using tools from strongly-coupled quantum field theories and supergravity. After reviewing the AdS/CFT correspondence in the introductory chapter 1, in chapter 2 we study 4d gauged supergravity theories that can be uplifted to 10d or 11d supergravity backgrounds. Motivated by results in the holographically dual 3d field theories, we examine the logarithmic corrections to the gravitational on-shell action and black hole entropy for a number of theories on different backgrounds, both supersymmetric and non-supersymmetric. By comparing our new results with the field theories' results, we have confirmed precision holography and found new Swampland constraints on the gravity theories. In Chapter 3, we study a specific 4d N=2 superconformal gauge theory called the E theory. This theory is closely related to the N=4 super Yang-Mills theory and has a holographic description in terms of type IIB supergravity on a Z2 orientifold of AdS5 x S5. With novel high precision numerics, we evaluate the partition function on S4, extremal correlators, and vacuum expectation values of Wilson loops with general 't Hooft coupling in the planar limit. Based on these numerics, we arrive at closed-form formulas in the strong coupling expansion. Our results match the literature on type IIB supergravity. In chapter 4, we study the Hawking-Page phase transition between two asymptotically locally AdS8 families of backgrounds, which are analogs of NUT and Bolt in the 4d counterpart. The backgrounds are parametrized by a squashing parameter of the asymptotic boundary, which is a squashed seven-sphere. Surprisingly, we observe the absence of the Hawking-Page transition, giving a prediction for the dual non-supersymmetric field theory. We also calculate and compare the free energies as a function of the squashing parameter in conformally coupled scalar, free fermion, and the holographic theory.