Untersuchung von Quantengravitation durch Holographie

Constructing a quantum theory of gravity has been the Holy Grail for research in theoretical physics for several decades. We need to understand quantum gravity to answer very important questions about the origin of the universe and properties associated with black holes that have mystified scientists for long. String theory is the most successful of the current attempts at building a theory of quantum gravity. One of its remarkable achievements is the discovery of the AdS/CFT correspondence and hence concrete exemplification of the Holographic Principle. The Holographic Principle states that all information about a theory of quantum gravity can essentially be recovered from its hologram, a theory without gravity, which lives on its boundary. The AdS/CFT correspondence realises this by relating a gravitational theory in curved Anti de Sitter (AdS) spacetime to a conformal field theory (which is a scale invariant quantum field theory) living on its boundary. The community of theoretical physics has seen enormous activity in studying various aspects of this correspondence. Although a formal proof of the conjecture is still lacking, the innumerable tests have even skeptics believing in the correctness of AdS/CFT. Using the correspondence, we have enriched our understanding of strongly coupled field theories using calculations in classical gravity. Surprisingly however, there has been hardly any progress in addressing issues of quantum gravity through AdS/CFT using weakly interacting conformal theories. This is where this project aims to make a substantial contribution. Recent holographic dualities, relating gravitational theories in AdS with higher spin fields (spins greater than two; spin two is usual gravity) and simple quantum field theories (conformal theories with higher symmetry structures) on the boundary of AdS, have opened a new direction in studying the quantum nature of gravity in simplified examples where symmetries can provide analytical handle on complicated computations. This project aims to first put these dualities on a firm footing and then use them to answer some of the outstanding questions in quantum gravity mentioned above related to the origin of the universe and properties of black holes. We wish to address how higher spin holography might be instrumental in resolving the big bang singularity and answering questions about black hole entropy in controlled examples, thus providing concrete steps in understanding the problems in their entirety. We also expect that our findings would shed light on the mysterious workings of the holographic principle helping us understand this fascinating tool.