Maximally supersymmetric backgrounds

Naturally our first goal was to settle the case of trivial holonomy group, which corresponds to the maximally supersymmetric backgrounds. Our working conjecture was that no new solutions would exist apart from the flat vacuum and the Freund-Rubin solutions AdS7 x S4 and AdS4 x S7. On hindsight this was naive and indeed it didn't take us long to realise that there was another maximally supersymmetric background: an indecomposable lorentzian symmetric space with solvable transvection group, of the kind classified by Cahen and Wallach in the late 1960s. The geometry of this background describes a plane-wave solution. In the process of writing the paper with our "new" results, we came across the 1984 paper of Kowalski-Glikman, which took considerable wind out of my sails at the time. The result of the ensuing damage limitation exercise is our joint paper Homogeneous fluxes, branes and a maximally supersymmetric solution of M-theory.

In the Fall of 2001, I co-organised the programme Mathematical aspects of string theory at the Erwin Schrödinger Institute in Vienna. It was during this time that together with Matthias Blau, Chris Hull, and George Papadopoulos, we looked for a maximally supersymmetric plane-wave solution to IIB supergravity. (George and I had already proved that no such solution could exist in type IIA.) It didn't take us long to find this solution, which is described in A new maximally supersymmetric background of IIB superstring theory. Although the results were obtained in the supergravity approximation, we conjectured, based on similar results both for plane-wave backgrounds as well as for maximally supersymmetric backgrounds, that this supergravity background would receive no α' corrections and hence be an exact superstring background. This would be confirmed shortly thereafter by Ruslan Metsaev who quantised the IIB superstring in this background and computed the spectrum.

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