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

TL;DR

This paper investigates the four-dimensional reduction of R^4 terms from ten-dimensional string theories, revealing two independent R^4 combinations at one loop in type IIA and heterotic theories, challenging previous beliefs.

Contribution

It demonstrates the existence of two independent R^4 terms in four-dimensional string effective actions, originating from M-theory, and explores their supersymmetrization when coupled to scalar multiplets.

Findings

Two independent R^4 combinations at one loop in type IIA.

Presence of similar R^4 terms in heterotic theories.

New R^4 term emerges with scalar multiplet coupling.

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.