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We dimensionally reduce the symmetries of the action to write down symmetries of the Hitchin system and further, we extend the construction to the supersymmetric, self dual theory. We review recent developments in the approach to calculating N=4 Yang Mills scattering amplitudes using symmetry arguments. Super conformal symmetry and the recently discovered dual super conformal symmetry have been shown to be related as a Yangian algebra and moreover, anomalous terms appearing in their action on amplitudes lead to deformations of the generators which gives rise to recursive relationships between amplitudes..

Just try. You gotta try. Don’t say, ‘I don’t want to do this, because, whatever.’ Don’t give up on something. A conformal basis (with rational coefficients) is used to extract amplitude integrands for both six and seven particles up to two loops more precisely, the complete one loop amplitude and parity even two loop amplitude (at two loops, we use a refined prescriptive basis). We also construct an alternative six point one loop basis involving integrands with conformal cross ratio coefficients, and reverse the duality to algebraically extract integrands from an ansatz, by introducing the Gram determinant. We expect the former approach to be applicable to n points at arbitrary loop order l, by going to one extra order of perturbation in the correlator (to determine all parity odd l loop ambiguities)..

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