Minimal unitary representations of space-time symmetries, AdS/CFT dualities and higher spin (super)-algebras

by Mr Murat Gunaydin

Thursday 3 Apr 2014, 11:30 → 12:30 Europe/Berlin

Seminar Room 3 (DESY, building 1b)

I will first review the twistorial oscillator construction of unitary representations of space-time symmetry (super-) algebras that underlie AdS/CFT dualities. Then I will discuss the novel geometric nonlinear realizations of spacetime (super)-groups as quasiconformal groups. Quasiconformal actions lead to a unified approach to minimal unitary realizations of noncompact symmetry algebras and super-algebras and their deformations. Minimal unitary representations and their deformations describe massless conformal fields in the respective dimensions. The minimal unitary realizations of 4 and 6 dimensional conformal groups and their deformations can be written as bilinears of some deformed twistors that transform nonlinearly under the Lorentz group. I will discuss how these novel realizations lead to a one parameter family of higher spin (super-)algebras in four dimensions labelled by heliciity. In six dimensions one finds a discrete infinite family of higher spin (super-)algebras labelled by the spin of an SU(2) symmetry which is the 6d analog of helicity.