- Tonight at 19:30, Paul Townsend (Cambridge, DAMPT) will kick off this year's series of the famous Colloquium Ehrenfestii. These lectures are organized about eight times a year, in the main auditorium of the Oort building.
Let's Twist Again - Revisiting the relation between supersymmetry, twistors and the division algebras
The Lorentz and conformal algebras in spacetime dimension D=3,4,6,10 are isomorphic to Sl(2;K) and Sp(4;K) for K=R,C,H,O, the four division algebras (the definitions are non-standard for K=O because octonionic multiplication is not associative). These are also the dimensions that allow a super-Yang-Mills theory, for which the free-field
limit can be found by quantization of the massless superparticle.
Many years ago it was found that the D=3,4,6 massless superparticle has a manifestly superconformal formulation in terms of supertwistors; i.e. spinors of the superconformal group. The mass-shell constraint is replaced by U(1;K) ``spin-shell’’ constraints that determine the supermultiplet helicities. More recently, a supertwistor formulation has been found for the massive superparticle, which can be viewed as a special case of the massless superparticle in D=4,6,10,11. The mass-shell constraint is now replaced by U(2;K) constraints which imply that the quantum superparticle describes a (massive) supermultiplet of zero "superspin".
An account will be given of this circle of ideas relating division algebras supersymmetry and twistors in the simple context of particle mechanics.
Publ. 30-09-2015 10:58