The Supersymmetric Effective Action of the Heterotic String in Ten Dimensions

TL;DR

This paper constructs the supersymmetric completion of quartic curvature and gauge invariants in the ten-dimensional heterotic string effective action, revealing new invariants and constraints related to anomaly cancellation.

Contribution

It provides the first explicit supersymmetric completions of quartic R and F invariants in heterotic string theory, including generalizations to supergravity coupled with supersymmetric Yang-Mills.

Findings

Two supersymmetric invariants with known bosonic parts are obtained.

One invariant generalizes to include gauge fields, forming an R+F^2+F^4 invariant.

The (3)R^4 term from string theory cannot be supersymmetrized.

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 $R+F^2+F^4$-invariant for supersymmetric Yang-Mills theory coupled to supergravity. Supersymmetry requires the presence of $B\wedge R\wedge R\wedge R\wedge R$-terms, ($B\wedge F\wedge F\wedge F\wedge F$ for Yang-Mills) which correspond to counterterms in the Green-Schwarz anomaly cancellation. Within the context of our calculation the $\zeta(3)R^4$-term from the tree-level string effective action does not allow supersymmetrization.