"The concept of symmetry has always been a powerful guide in the formulation of fundamental interactions. It will certainly be crucial in one of the main challenges of contemporary physics : reconcile General Relativity and quantum mechanics. In this context, the understanding of the fate of cosmological singularities and of the very nature of spacetime is puzzling. It has been shown that gravitational theories are naturally related to hyperbolic Kac-Moody algebras in the BKL limit, i.e. in the vicinity of cosmological singularities. More precisely, the asymptotic dynamics of the fields is equivalent to that of a free massless particle interrupted by collisions against infinite potential walls. The set of walls determine a « billiard plane » which is, for particular theories, identifiable with the fundamental Weyl chamber of some Kac-Moody algebras. To analyse further this connection, coset actions explicitly invariant under these Kac-Moody algebras have been constructed and compared with (super)gravity theories. Partial results enforce this gravity/coset correspondence. To make further progress, an approach able to deal with quantum effects will certainly be enlightening. A window to a quantum description of singularities is opened by the celebrated AdS/CFT conjecture which is a realisation of the holographic principle in string theory. Our purpose is to analyse the cosmological singularities via the AdS/CFT correspondence and to search for the Kac-Moody algebraic structure in the dual picture. In this perspective we will generalise the known big bang/big crunch solutions with AdS boundary conditions and investigate their CFT dual. Next, to recover the Kac-Moody algebras in the dual approach, we will establish a dictionary between the ''Billiard description"" and ""CFT quantities"". This will bring new tools to understand the very meaning of resolving singularities and a path towards the idenfication of the symmetries of quantum gravity."
Field of science
- /natural sciences/mathematics/pure mathematics/algebra
- /natural sciences/physical sciences/string theory
- /natural sciences/physical sciences/quantum physics
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