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

Filipe Moura
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Abstract

We analyze the reduction to four dimensions of the R^4 terms which are part of the ten-dimensional string effective actions, both at tree level and one loop. We show that there are two independent combinations of R^4 present, at one loop, in the type IIA four dimensional effective action, which means they both have their origin in M-theory. The d=4 heterotic effective action also has such terms. This contradicts the common belief thathere is only one R^4 term in four-dimensional supergravity theories, given by the square of the Bel-Robinson tensor. In pure N=1 supergravity this new R^4 combination cannot be directly supersymmetrized, but we show that, when coupled to a scalar chiral multiplet (violating the U(1) $R$-symmetry), it emerges in the action after elimination of the auxiliary fields.

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Filipe Moura. 2007-06-12. Type II and heterotic one loop string effective actions in four dimensions. https://doi.org/10.1088/1126-6708%2F2007%2F06%2F052

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