The supersymmetric effective action of the heterotic string in ten dimensions

Abstract

We construct the supersymmetric completion of quartic R+R 4 -actions in the ten-dimensional effective action of the heterotic string. Two invariants, of which the bosonic parts are known from one-loop string amplitude calculations, are obtained. One of these invariants can be generalized to an R+F 2

Heterotic — type I superstring duality and low-energy effective actions

“…Indeed, J 1 is a combination of R 4 , F 4 , R 2 F 2 type D = 10 super-invariants recently constructed in [24,25]. According to [24,25] the bosonic parts of a set of 6 independent superinvariants are given by (an invariant action should start with R + trF 2 -terms) which all contain parity-odd terms, and also by the parity-even combination J 0 in (3.5).…”

“…According to [24,25] the bosonic parts of a set of 6 independent superinvariants are given by (an invariant action should start with R + trF 2 -terms) which all contain parity-odd terms, and also by the parity-even combination J 0 in (3.5). Note also that…”

“…This is necessary for consistency of the duality conjecture and is probably related to the special property of D = 10 supersymmetry that certain superinvariants of given dimension may have only specific dilaton dependence [24,9]. Indeed, the dilaton plays a special role in D = 10 supergravity, being in the same multiplet with graviton.…”

“…We shall see that the relation between the R 4 corrections is more complicated than between the F 4 terms, reflecting the existence of several super-invariants containing R 4 contractions [30,24,25].…”

On anomaly-free supergravity as an effective string theory

“…An argument in favour of the latter suggestion is that this term can be separately supersymmetrized, at least if an (off-shell) superfield exists [19]. However, in a very recent paper by de Roo et al [20] it is argued that the supersymmetrization clashes with gauge-invariance if only physical fields are present, while there is no such problem with the similar R 4 term coming from string loops [21]. It is then very tempting to believe that what we have is the full effective theory corresponding to the tree level heterotic string, the apparent contradiction found in [20] perhaps being resolved by the addition of higher-order corrections to the supersymmetry transformations, and that loop effects would be accounted for by the addition of non-minimal terms.…”