Sunday, July 22, 2012

Twistors and N=8 Supergravity

Cachazo, Mason and Skinner have given a formula (and its proof) for the complete tree-level S-matrix of N=8 supergravity, using twistor techniques.  As is known, the BCFW recursion relations were initially used to study gluon amplitudes.  Later it was shown that gravity amplitudes also obey such recursion relations.  In N=4 super Yang-Mills BCFW decomposition is related to performing a contour integral in the moduli space of holomorphic maps so as to localize on the boundary where the worldsheet degenerates to a nodal curve.  The summands on the right hand side of the recursion relation correspond to the various ways the vertex operators and map degree may be distributed among the two curve components (see above picture). 

The formula is a big step in moving towards a motivic formulation of gravity.  Moreover, as N=8 supergravity in four dimensions can be recovered from a toroidal compactification of M-theory, it would be interesting to understand the formula in an 'oxidized' context in eleven dimensions.

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