One loop superstring effective actions and d=4 supergravity

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We review our recent work on the existence of a new independent R^4 term, at one loop, in the type IIA and heterotic effective actions, after reduction to four dimensions, besides the usual square of the Bel-Robinson tensor. We discuss its supersymmetrization.
1+7 pages. Work presented at the XVI International Fall Workshop on Geometry and Physics, Lisbon, Portugal, September 2007

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