Type II and heterotic one loop string effective actions in four dimensions

We analyze the reduction to four dimensions of the R^4 terms which are partof the ten-dimensional string effective actions, both at tree level and oneloop. We show that there are two independent combinations of R^4 present, atone loop, in the type IIA four dimensional effective action, which means theyboth have their origin in M-theory. The d=4 heterotic effective action also hassuch terms. This contradicts the common belief thathere is only one R^4 term infour-dimensional supergravity theories, given by the square of the Bel-Robinsontensor. In pure N=1 supergravity this new R^4 combination cannot be directlysupersymmetrized, but we show that, when coupled to a scalar chiral multiplet(violating the U(1) $R$-symmetry), it emerges in the action after eliminationof the auxiliary fields.Comment: v2: 22 pages. Discussion on the new R^4 term and extended supergravity has been abridged and improved. Published versio