ar X iv : 0 71 1 . 32 28 v 1 [ he p - th ] 2 1 N ov 2 00 7 One loop superstring effective actions and d = 4 supergravity
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چکیده
We review our recent work on the existence of a new independent R4 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 R4 terms in ten dimensions The superstring α effective actions contain two independent terms X,Z which involve only the fourth power of the Weyl tensor, given by X := t8t8W, Z := −ε10ε10W. (1) For the heterotic string two other R4 terms Y1 and Y2 appear at order α [1, 2, 3]: Y1 := t8 ( trW )2 , Y2 := t8trW = X 24 + Y1 4 . (2) Each t8 tensor has eight free spacetime indices, acting in four two-index antisymmetric tensors as defined in [4, 5]. The effective action of type IIB theory must be written, because of its well known SL(2,Z) invariance, as a product of a single linear combination of order α invariants and an overall function of Ω = C + ie, C being the axion and φ the dilaton. The R4 terms of this effective action are given in the string frame by 1 √−gLIIB ∣
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تاریخ انتشار 2008