Four dimensional R^4 superinvariants through gauge completion.pdf

a r X i v : h e p - t h / 0 2 0 6 1 1 9 v 3 3 S e p 2 0 0 2 YITP-SB-02/26 Four dimensional R4 superinvariants through gauge completion Filipe Moura C. N. Yang Institute for Theoretical Physics State University of New York Stony Brook, NY 11794-3840, U.S.A fmoura@insti.physics.sunysb.edu Abstract We fully compute the N = 1 supersymmetrization of the fourth power of the Weyl tensor in d = 4 x-space with the auxiliary fields. In a previous pa- per, 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 N = 1 actions, in four dimensions, that contain pure R4 terms (with coupling constants). We explicitely write these actions in terms of the θ components of the chiral density ? and the supergravity superfields R,Gm,WABC . Using the method of gauge comple- tion, we compute the necessary θ components which allow us to write these actions in x-space. We discuss under which circumstances can these extra R4 correction terms be reabsorbed in the pure supergravity action, and their relevance to the quantum supergravity/string theory effective actions. February 1, 2008 1 Introduction In a previous paper [1], we wrote and analyzed in d = 4,N = 1 superspace a lagrangian which contained a pure R4 term: L = 1 2κ2 ∫ E ( 1 + αW 2W 2 ) d4θ (1.1) This lagrangian could be seen as a four dimensional N = 1 string/M-theory effective action, resulting from a compactification and truncation from ten/eleven dimensions. In that case the constant α κ2 could be identified up to a factor with α′3, α′ being the string slope parameter. Originally the αW 2W 2 term of this lagrangian was thought of as a possible three- loop quantum correction to supergravity. In reference [2] it was shown that super- symmetry implies the one and two-loop finiteness of supergravity, but there exists a potential non-vanishing on-shell superinvariant which could mean non-finiteness of