Abstract:We consider the application of twistor theory to five-dimensional anti-de Sitter space. The twistor space of AdS 5 is the same as the ambitwistor space of the fourdimensional conformal boundary; the geometry of this correspondence is reviewed for both the bulk and boundary. A Penrose transform allows us to describe free bulk fields, with or without mass, in terms of data on twistor space. Explicit representatives for the bulkto-boundary propagators of scalars and spinors are constructed, along with twistor action functionals for the free theories. Evaluating these twistor actions on bulk-to-boundary propagators is shown to produce the correct two-point functions.
We construct a minitwistor action for Yang-Mills-Higgs theory in three dimensions. The Feynman diagrams of this action will construct perturbation theory around solutions of the Bogomolny equations in much the same way that MHV diagrams describe perturbation theory around the self-dual Yang Mills equations in four dimensions. We also provide a new formula for all tree amplitudes in YMH theory (and its maximally supersymmetric extension) in terms of degree d maps to minitwistor space. We demonstrate its relationship to the RSVW formula in four dimensions and show that it generates the correct MHV amplitudes at d = 1 and factorizes correctly in all channels for all degrees. * F = DΦ .(1.3) 1 In the presence of monopoles, this term is a topological invariant.
DISCUSSIONJ1( .(.ili'(l. This is so because setting x = 0 or // = 0 in equation i:it' gives an integrand of the same form as the integrand in equation 111). The integration proceeds as for equation (37) ;,]),! ea-ily leads to the conclusion that i>/ } is continuous over the philips,/' = 0 and •// = 0.
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