Quantum gravity from the boundary Holographic properties of symmetric product orbifolds

One of the biggest open problems within theoretical physics regards a theory of quantum gravity. This thesis studies quantum gravity through the framework of AdS/CFT, which is a duality between quantum gravity on theories with a negative cosmological constant (AdS), and a conformal field theory (CFT) that lives on the boundary of those universes. Through the duality any question in an AdS universe can be translated to a question in the corresponding CFT, which does not contain gravity. The perspective we take in this thesis is that the space of CFTs defines the space of quantum gravity theories on AdS through the correspondence. The theories of quantum gravity that are of most interest are those that resemble the physics we observe in our universe, where at low energies an effective description of weakly-coupled semiclassical general relativity emerges. CFTs dual to such theories are called holographic. We can thus study interesting theories of quantum gravity by finding and studying properties of holographic CFTs. We focus on CFTs constructed via symmetric product orbifold. Such CFTs have various favorable properties in light of holography, but they cannot be holographic. They can however lead to interesting moduli spaces which can contain holographic points. We study various aspects of the theories on the moduli spaces, such as the response of symmetries under deformations, possible matter interactions, and we study the elliptic genus, a signed count of 1/4-BPS states that is constant on moduli space. We classify symmetric product orbifold CFTs according to the holographic properties of their moduli spaces, and find sensitive dependence on the seed CFT.