Speaker: Philippe Spindel (UMons)

Location: VUB D2.13

Start: 10h30

Several aspects of the quantum dynamics of a supersymmetric ``squashed three-sphere" by dimensionally reducing (to one timelike dimension) the action of $D=4$ simple supergravity for an $SO(3)$-homogeneous (Bianchi IX) cosmological model will be discussed. One finds that the quantum Hamiltonian is built from operators that generate a 64-dimensional representation of the (infinite-dimensional) maximally compact sub-algebra of the rank-3 hyperbolic Kac-Moody algebra $AE_3$. Some exponentials of these operators generate a spinorial extension of the Weyl group of $AE_3$ which describe (in the small wavelength limit) the chaotic quantum evolution of the universe near the cosmological singularity.
ref.:  [arXiv : 1304.6381, Class. Quantum Grav. 30 (2013) 162001]