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

TL;DR

This paper investigates the duality between heterotic and type I superstring theories by comparing their low-energy effective actions, focusing on the order R^4 terms and their loop corrections, revealing consistency conditions for duality.

Contribution

It provides a detailed comparison of R^4 terms in heterotic and type I superstring effective actions, highlighting the non-renormalization properties and the implications for duality.

Findings

Certain R^4 terms do not receive higher-loop corrections due to supersymmetry.

The tree-level R^4 term must appear at all orders, scaled by a function of the dilaton.

Duality consistency constrains the form of loop corrections in the effective actions.

Abstract

We compare order $R^4$ terms in the 10-dimensional effective actions of SO(32) heterotic and type I superstrings from the point of view of duality between the two theories. Some of these terms do not receive higher-loop corrections being related by supersymmetry to `anomaly-cancelling' terms which depend on the antisymmetric 2-tensor. At the same time, the consistency of duality relation implies that the `tree-level' $R^4$ super-invariant (the one which has $\zeta(3)$-coefficient in the sphere part of the action) should appear also at higher orders of loop expansion, i.e. should be multiplied by a non-trivial function of the dilaton.