Higher spin-gravity, holography and integrability

Einstein`s general relativity describes gravity at macroscopic scales, while Schrödinger`s and Heisenberg`s quantum mechanics describes physics at microscopic scales. To describe gravity at microscopic scales, it is thus necessary to unify general relativity and quantum mechanics. By the early 1980`s, physicists realized that nearly all such unified theories are afflicted by internal inconsistencies. String theory is one exception to this and is currently considered as the most promising approach to unification. By construction, string theory has very intricate structures. As such, it is imminent to develop a variety of theoretical tools for unravelling these intricacies before we conclude that string theory is the final theory of quantum gravity. The particle transmitting the gravitational force is known as "graviton". Like other elementary particles, the graviton has a certain "spin", an intrinsic kind of angular momentum. According to quantum mechanics, spin takes multiples of half-integer, e.g. it is 0 for the hypothetical Higgs, 1/2 for the electron and proton, 1 for the light- particle (photon) and 2 for the graviton. In flat space-time, it was rigorously proven that elementary particles with spin higher than 2 cannot exist. Interestingly, in curved space-times which provide the adequate description of gravity according to Einstein`s theory elementary particles with higher spin can exist. The theory describing interactions between higher spin particles and graviton is called "higher spin gravity". Higher spin gravity theories constitute a middle ground between string theory and general relativity. They are considerably simpler than full-fledged string theory yet have considerably more structure than general relativity. Thus, they may provide useful models for quantum theory of gravity that avoid several of the complications arising in attempts to directly quantize Einstein gravity, while simultaneously avoiding the technical complications that come with a fully stringy description which currently is not available. Three-dimensional higher spin theories are particularly interesting in this context, since they allow significant further simplifications. An outstanding aspect of these theories is that they often correspond "holographically" to theories without gravity, formulated in one dimension lower hence the name "holographically", since one can choose, depending on the problem one would like to investigate, if the physical data are interpreted in a three-dimensional way (like the three-dimensional object represented by a hologram) or in a two-dimensional manner (like the holographic screen, on which the hologram is displayed). The main purpose of our bilateral project between Seoul and Vienna is to establish and test new holographic correspondences between three-dimensional higher spin gravity theories and certain ("integrable") two-dimensional field theories. Due to the highly theoretical nature of the topics intense interaction among the scientists involved is crucial and will lead to mutual benefits at the respective research institutions in Seoul and Vienna.

The FWF project Higher spin gravity, holography and integrability studied a specific aspect of the broad question how general is the holographic principle? by suggesting new holographic correspondences between so-called higher spin theories and specific quantum field theories with an infinite number of symmetries.The holographic principle states that one can describe the same physical situation using two apparently different theories in different dimensions. The higher-dimensional theory is a quantum theory of gravity and the lower-dimensional one a quantum theory without gravity.Holography has become a cornerstone in research on the elusive theory of quantum gravity. It has a precise implementation within string theory through the so-called Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence by Maldacena. However, it is often difficult to perform detailed calculations in fully fledged string theory. Therefore, it is useful to consider approximations or limits of string theory that allow to resolve challenging theoretical issues, in particular in the context of quantum gravity.Higher spin gravity emerges formally in the tensionless limit of string theory. In terms of complexity, higher spin gravity is considerably simpler than string theory, and yet much more complicated than other approximations of string theory, like the supergravity approximation that has been used frequently in the past two decades.In this project we suggested and scrutinized new holographic correspondences between specific higher spin gravity theories in three dimensions and their dual field theories in two dimensions beyond the canonical AdS/CFT correspondence. We found that higher spin gravity is naturally suitable for non-AdS holography without the introduction of exotic matter fields that are usually needed, in particular so-called Lifshitz, Schrödinger or warped AdS holography.Perhaps the biggest surprise was our unexpected discovery of the first higher spin theory in flat space, which previously was believed to be impossible.The project relied on an international collaboration with Soo-Jong Rey in South Korea and led to mutual research visits of several team members of the project (faculty, postdocs and PhD students).