Four dimensional 4 superinvariants through gauge completion

doi:10.1088/1126-6708/2002/08/038

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Journal of High Energy Physics

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Filipe Moura JHEP08(2002)038 doi:10.1088/1126-6708/2002/08/038

Four dimensional ⁴ superinvariants through gauge completion

Filipe Moura¹

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We fully compute the Script N = 1 supersymmetrization of the fourth power of the Weyl tensor in d = 4 x-space with the auxiliary fields. In a previous paper, we showed that their elimination requires an infinite number of terms; we explicitely compute those terms to order κ⁴ (three loop). We also write, in superspace notation, all the possible Script N = 1 actions, in four dimensions, that contain pure Script R ⁴ terms (with coupling constants). We explicitely write these actions in terms of the θ components of the chiral density epsilon and the supergravity superfields R,G_m,W_ABC. Using the method of gauge completion, we compute the necessary θ components which allow us to write these actions in x-space. We discuss under which circumstances can these extra Script R ⁴ correction terms be reabsorbed in the pure supergravity action, and their relevance to the quantum supergravity/string theory effective actions.