Maths HEP supplementary seminars: SEMINAR CANCELLED DUE TO UNFORESEEN CIRCUMSTANCES - Minisuperpsace Quantum Supersymmetric Cosmology and its Hidden Hyperbolic Kac-Moody Structures.
14 September 2016 14:00 in CM221 (Mathematical Sciences)
One of the key challenges of gravitational physics is to understand the fate of spacetime at spacelike (cosmological) singularities, such as the big bang singularity that gave birth to our universe. A novel way of attacking this problem has been suggested a few years ago via a conjectured correspondence between various supergravity theories and the dynamics of a spinning massless particle moving on an infinite-dimensional Kac–Moody coset space. Evidence for such a supergravity/Kac–Moody link emerged through the study à la Belinskii– Khalatnikov–Lifshitz (, , ) of the structure of cosmological singularities in the string theory and supergravity, in space- time dimensions 4 to 11. It was found that, for the bosonic sector of eleven dimensional supergravity most of the degrees of freedom freeze, excepted the diagonal components of the metric which undergo at each point a chaotic billiard motion, in a cell of the hyperbolic space, equivalent to a conical polyhedron in a 10-D Lorenztian space, that can be identified with the Weyl chamber of E(10).
The hidden rôle of E(10) in the dynamics of maximal supergravity was confirmed to higher approximations (up to the third level) in the gradient expansion of its bosonic sector. In addition, the study of the fermionic sector of supergravity theories has exhibited a related rôle of Kac–Moody algebras. At leading order in the gradient expansion of the gravitino field, the fermionic dynamics at each spatial point was found to be given by parallel transport with respect to a (bosonic-induced) connection taking values within the compact sub-algebra of the corresponding bosonic Kac– Moody algebra. However, the latter works considered only the terms linear in the gravitino, and, moreover, treated the fermionic degrees of freedom as a “classical” (i.e. Grassman-valued) fermionic field.
During this talk I will discuss D=4 supergravity, and thus pass from E(10) to AE(3). The aim of my talk will be to clarify the occurrence of hidden Kac–Moody structures in simple supergravity, within a setting which goes beyond the previous works both by being fully quantum, and by taking completely into account the crucial nonlinearities in the fermions that allow supergravity to exist. On the other hand, our framework will simplify the cosmological dynamics by working within a supersymmetric minisuperspace model, namely a Bianchi IX one. Although the quantum theory of supersymmetric minisuperspace models has attracted the interest of many authors, we shall give here, in our knowledge for the first time, a complete description of all the physical states of the supersymmetric Bianchi IX model [, ]. In particular it shows that the quantized contribution of the terms quartic in the Fermions generically leads to an avoidance of the zero-volume singularity, i.e. to a cosmological bounce.
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