Flat space holography

One of the surprising predictions that came out of quantum gravity research is that we could live in fewer dimensions than we think we do. Bekenstein and Hawking famously showed in the 1970ies that black holes have an entropy proportional to their area, rather than their volume. Inspired by these results, `t Hooft and Susskind proposed the holographic principle in the early 1990ies, according to which a theory of quantum gravity in three dimensions should be equivalent to an ordinary quantum field theory in one dimension lower. In the late 1990ies Maldacena argued that the holographic principle is realized within string theory in a very specific way. This realization is known as `Anti-de Sitter/conformal field theory correspondence` (AdS/CFT) and has triggered numerous further ideas and developments in the past 1-2 decades. In all instances of AdS/CFT the quantum gravity theory requires a negatively curved space. However, the original considerations that led `t Hooft and Susskind to formulate the holographic principle had nothing to do with negatively curved space. In fact, if their holographic principle captures a true fact about Nature, then holography must work also in flat space. The main purpose of the project is to check to which extent this is true. In particular, we intend to establish and scrutinize new holographic correspondences between (quantum) gravity theories in flat space and quantum field theories without gravity. Such correspondences provide unexpected connections among theories in different dimensions that at first glance are completely unrelated, leading to a possible cross-fertilization between otherwise disconnected branches of physics.

One of the surprising predictions emerging from quantum gravity research is that we could live in fewer dimensions than we think we do. Bekenstein and Hawking famously showed in the 1970ies that black holes have an entropy proportional to their area, rather than their volume. Inspired by these results, t Hooft and Susskind proposed the holographic principle in the early 1990ies, according to which a theory of quantum gravity in three dimensions should be equivalent to an ordinary quantum field theory in one dimension lower. In the late 1990ies Maldacena argued that the holographic principle is realized within string theory in a very specific way. This realization is known as Anti-de Sitter/conformal field theory correspondence (AdS/CFT) and has triggered numerous further ideas and developments in the past two decades. In all instances of AdS/CFT the quantum gravity theory requires a negatively curved spacetime.However, the original considerations that led t Hooft and Susskind to formulate the holographic principle had nothing to do with negatively curved space. In fact, if the holographic principle captures a true fact about Nature, then holography must work also in flat space.The main purpose of the project was to check to which extent this is true. In particular, we established and scrutinized new holographic correspondences between (quantum) gravity theories in flat space and quantum field theories without gravity. Such correspondences provide unexpected connections among theories in different dimensions that at first glance are completely unrelated, leading to a cross-fertilization between otherwise disconnected branches of physics.In the framework of the FWF-project Flat space holography one postdoc and four PhD stu- dents were hired at TU Wien. Around 30 scientific publications and as many theses (PhD, master, bachelor) were finished (see Part II for details on the project and Part III for details on publications and further results of the project).