EXACT HOLOGRAPHY · Towards an exact holographic non-AdS/non-CFT correspondence: black holes and gauge theories

Towards an exact holographic non-AdS/non-CFT correspondence: black holes and gauge theories

A longstanding challenge in modern theoretical physics is the unification of two major theories of the twentieth century: general relativity and quantum mechanics. A far-reaching and revolutionary paradigm in this context is the so-called holographic principle, suggesting that theories of quantum gravity in a d-dimensional space-time may equivalently be described in terms of non-gravitational theories in one dimension less. Two seemingly distinct paths, string theory and gravity in lower dimenions, have allowed for a more precise formulation of the holographic principle, eventually leading to the concept of gauge / gravity duality (or AdS/CFT correspondence). The latter led to crucial conceptual advances in two fundamental questions: the understanding of the strong coupling dynamics of gauge theories and that of the microscopic nature of black holes. As it stands, the original correspondence applies to a limited class of situations, although many steps have been taken towards extending it. On both gauge theory and gravity sides, it involves very 'symmetric' setups. The objectives are to gain insights on the less symmetric field theories observed in nature on the one hand, and to describe astrophysical black holes (in particular, non supersymmetric) on the other hand. Dramatic new developments in this direction have appeared and further extended over the last three years under the name 'Kerr/CFT correspondence', suggesting that astrophysical back hole could be describable in terms of a two-dimensional (2D) conformal field theory. The gauge / gravity correspondence has furthemore experienced a ?ow of groundbreaking new ideas recently, in that it was suggested that the duality could be used to describe more general strongly coupled systems and phenomena (e.g. non-relativistic conformal invariance, superconductivity, quantum critical points). The latter aspect is currently receiving a huge amount of attention, since it points towards the exciting possibility of testing some aspects of the conjecture experimentally. Interestingly enough, these ideas appear to be closely related to a three-dimensional gravity theory, topologically massive gravity (TMG), of which a particular sector has been proposed to be exactly quantisable. In these scenarios, a family of spaces known as warped AdS3 spaces (WAdS3) plays a crucial rule. Not only are they ubiquitous in all recent applications of the gauge / gravity duality mentioned above, but they also appear in TMG -a lower-dimensional gravity model- where they have been conjectured to be dual to certain CFTs in two dimensions. The general framework of this project has been to explore the properties of these new and promising holographic setups, in taking two complimentary approaches - lower-dimensional gravity models and string theory. Using the former, we were able to define a semi-classical phase space for the three types of WAdS3 spaces (null, spacelike and timelike) in TMG. This was done by determining a consistent set of boundary conditions including in particular a family of warped black holes solutions. We determined the asymptotic symmetries associated with these boundary conditions and in the null warped case we also studied the linear stability of the black hole solutions. In the timelike and spacelike cases, the asymptotic symmetries only reveal the existence of one copy of a Virasoro algebra (while two would be expected for a full-fledged two-dimensional CFT) whose central charge, however, matches the one predicted by Anninos et al. This result is important in that it open the perspective of a new class of gauge / gravity dualities, where the dual field theory does not exhibit full conformal symmetry. In the null case, a similar reasoning allowed us to conjecture that the dual theory would be a chiral CFT of which we computed the central charge. In the complementary context of string theory, we exploited the observation that WAdS3 spaces are part of the target space of an exact string theory background, through a marginal deformation of the SL(2,R)xSU(2)xU(1)4 Wess-Zumino-Witten model. Having a control over the worldsheet theory, we were able to use techniques inspired by Giveon-Kutasov-Seiberg to relate worldsheet to spacetime charges. We showed that generically, only one spacetime Virasoro algebra could be constructed, in accordance with our previous analysis. However, we observed that at a certain discrete sets of points in moduli space, a second Virasoro algebra did appear. This result is surprising but indicates that in some special cases WAdS3 spaces could indeed be dual to a 2D CFT. We furthermore studied another class of deformations, which is a lower-dimensional analog of the supersymmetry breaking versions of AdS/CFT. In that case, we could explain the origin of the breaking from the worldsheet theory, and obversed supersymmetry enhancements at discrete points in moduli space. In another work, we proposed a duality relating quantum gravity in space-times with cosmological horizons -warped de Sitter spaces- and a field theory. The results obtained in the framework of this project have generated significant interest and have been extensively discussed at various occasions (talks, seminars, invitations). They have given birth to numerous long-lasting collaborations, linking the return institution to some of the top institutions in the world, and led to publications in the best scientific journals in the field. They laid the foundations for a variety of new paths to explore, in particular in the context of Kerr/CFT and holographic condensed matter. Some of these aspects are currently under further investigation namely with colleagues at Harvard, where I was hired by Prof. A. Strominger as a postdoctoral fellow at the end of my Marie Curie fellowship. My objective is now to obtain a permanent position at my return institution, where I could further share the experience gained in various fields. Fundamental research has by definition no direct foreseeable socio-economic impact, although mid- to long-term derived applications are of course not excluded.

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