Matthieu VILATTE

PhD Student

Research group: String Theory  

Thesis: "Conformal Field Theories, holography fluid/gravity and the asymptotic structure of the gravitation"

Advisors: Marios Petropoulos et Anastasios Petkou

Research

CFT, AdS/CFT in fluid framework, flat holography, Carrollian fluids

The thesis is an international cotutelle between the CPHT and the Department of Physics of Aristotle University of Thessaloniki (Greece) with Anastasios Petkou. The global project splits in two parts, each one being linked to Conformal Field Theories (CFT) and their consequences in gravitational theories via the holography AdS/CFT or in statistical physics.

The AdS/CFT paradigm was firstly designed by Juan Maldacena in the 90s. It postulates that under certain hypotheses there is an equivalence between a gravitational theory in the bulk of a dimension D closed Riemannian manifold, negatively curved (the so-called AdS spaces), and a CFT on the D-1 dimensional boundary. The holographic principle is well understood for AdS paces for which the degrees of freedom on the boundary can be recast as a relativistic fluid. Einstein’s equations are thus equivalent to the covariant conservation of the fluid energy momentum tensor. Conversely, if we give us a fluid on the boundary it is possible to recover the corresponding solution in the bulk. Recently, given that observations tend to prove the asymptotic flatness of our Universe, the main goal was to extend the holographic principle to flat manifolds where one sees the emergence of a new type of fluids invariant under the Carroll group (limit of vanishing speed of light of the usual Poincaré group). The thesis focuses on improving our knowledge on this Carrollian fluids and on our comprehension of flat holography.

The second project deals more specifically with CFTs and particularly the computation of thermal correlation function. In thermal theories, it is well known that we need to compactify one dimension of space time to get from the zero temperature field theory results for the finite temperature one. The state of knowledge shows an intriguing mathematical structure based on polylogarithm functions which are interesting to study to get a better understanding of the constraints imposed by the theory on thermal correlators. Some consequences for statistical physics systems are possible.