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

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.

v2: 22 pages. Discussion on the new R^4 term and extended supergravity has been abridged and improved. Published version

References in corpus (5)

• Three-Loop Superfiniteness of N=8 Supergravity
• Is N = 8 Supergravity Ultraviolet Finite?
• Ultraviolet properties of Maximal Supergravity
• Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity
• On the supersymmetric completion of the $R^4$ term in M-theory

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• N=2 higher-derivative couplings from strings
• Consistent truncations in higher derivative supergravity
• Starobinsky inflation beyond the leading order
• One loop superstring effective actions and N=8 supergravity
• Higher-order string effective actions and off-shell d=4 supergravity