We provide a supersymmetric generalisation of n quantum bits by extending the LOCC entanglement equivalence group [SU(2)]ⁿ to the supergroup [uOSp(2|1)]ⁿ and the SLOCC equivalence group [SL(2,C)]ⁿ to the supergroup [OSp(2|1)]ⁿ. We introduce the appropriate supersymmetric generalisations of the conventional entanglement measures for the cases of n=2 and n=3. In particular, super-GHZ states are characterised by a non-vanishing superhyperdeterminant.

The Salam-Sezgin model of D=6 supergravity provides a pathway towards interesting gauge groups and couplings after reduction further down to D=4. But the origin of this model from a string/M-theory perspective has remained obscure. In this talk, the problem will be addressed using a D=7 Horava-Witten construction, with particular attention to the type of bulk-boundary couplings required and the necessary classical noninvariances needed to compensate for quantum gauge and supersymmetry anomalies.

Recently, there has been remarkable progress in the analysis of multi-loop amplitudes in supergravity in various dimensions using string theory and in field theory methods. There are strong indications that four-dimensional maximal supergravity theories have a better ultraviolet behavior than expected from a conservative implementation of on-shell superspace that is an intricate consequence of gauge invariance and supersymmetry. The N=8 supergravity amplitudes have a much simpler structure than could be guessed from a traditional approach based on Lagrangians and Feynman graphs, and display striking similarities with N=4 super-Yang-Mills amplitudes. In this talk we will analyze the constraints from supersymmetry and gauge invariance on the ultraviolet behavior of maximally supergravity gauge theories in various dimensions. We will also compare the ultraviolet behavior of N=4 super-Yang-Mills amplitudes at higher-loop orders in the leading and subleading color factors with the expectations for N=8 supergravity amplitudes in various dimensions.