Week 29.11.2009 – 05.12.2009

A pedagogical introduction into the ideas, propects and successes of spacetime quantization will be presented, with emphasis on what it tells us about hte problems of quantizing gravity and renormalizing quantum field theory.

We give a method of deriving the field-strengths of all massless and massive, i.e. gauged, maximal supergravity theories in any dimension starting from the Kac-Moody algebra E11. Considering the subalgebra of E11 that acts on the fields in the non-linear realisation as a global symmetry, we show how this is promoted to a gauge symmetry enlarging the algebra by the inclusion of additional generators. Given the enlarged algebra corresponding to the massless theory, we show that this can be deformed to obtain the algebra corresponding to the gauged theory. We show how this works in detail for the case of Scherk-Schwarz reduction of IIB to nine dimensions. We then classify all the possible deformations in any dimensions and show that these are in one to one correspondence with all the possible gauged supergravities. This provides a very efficient, simple and unified derivation of the field strengths and gauge transformations of all the bosonic fields of any maximal supergravity theory.

In this talk we will review the appearance of an infinite dimensional symmetry algebra of tree level scattering amplitudes of N=4 super Yang-Mills theory, known as the Yangian of psu(2,2 4). It arises through the commutation of standard superconformal and the recently discovered dual superconformal symmetries of scattering amplitudes. At the loop level the conformal and dual conformal symmetry is destroyed by infrared divergencies. The present challenge is whether it may be repaired. We point out a novel IR regularization based on a suitable Higgsing of the theory, which is natural from the dual string perspective. It turns out that in this regularization an extended conformal symmetry of the loop amplitudes arises, which remains free of anomalies.