Holography is by now a fundamental tool in the understanding of both strongly coupled conformal field theories (CFTs) and quantum theories of gravity. While holography in Anti de Sitter (AdS) space-times is rather well understood, we currently lack a basic picture of what it means in non-AdS space-times. Considering non-AdS space-times is an essential and urgent next step in the study of quantum gravity as we seem to live in a universe with a positive cosmological constant that is approaching de Sitter (dS) in the far future. Also, the near-horizon geometries of black holes are typically described by more exotic geometries that need to be understood on their own right.
I propose to address this and study the physics of holographic systems on non-AdS space-times and their connection to generalized geometric structures that naturally arise in these setups. In order do this I will use both conventional field theory techniques and new holographic tools, some of which I have developed recently.
The relevance of GenGeoHol is illustrated by universal properties of black holes, e.g. their area-law entropy. These are independent of AdS, pointing towards the existence of a more general holographic principle that generalizes the usual symmetries and geometric notions. A great deal of evidence has accumulated recently indicating that this is indeed the case. The physics of extremal black holes and non relativistic systems are clear examples.
GenGeoHol will impact a wide range of fields. As one moves away from AdS Einstein gravity, the dual quantum-field theories present different symmetries from that of usual relativistic systems. These systems couple naturally to generalized background geometries which are of intrinsic interest and key to a range of concepts extending from Newton-Cartan geometry in non-relativistic systems to higher-spin geometries for so-called W_N CFTs.
Given my experience and track record, I am uniquely positioned to attack this problem successfully.
Fields of science
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