Non-Abelian Born-Infeld Action and Type I - Heterotic Duality (II): Nonrenormalization Theorems

TL;DR

This paper proves non-renormalization theorems for certain F^n couplings in heterotic string theory, confirming duality predictions and showing specific couplings are only generated at certain string loop levels.

Contribution

It establishes the vanishing of two-loop corrections to heterotic F^4 terms and shows F^5 and F^6 couplings are not renormalized at one loop, supporting duality conjectures.

Findings

Two-loop corrections to heterotic F^4 terms vanish.

F^5 and F^6 couplings are not renormalized at one loop.

Results hold in any heterotic vacuum with sixteen supercharges.

Abstract

Type I - heterotic duality in D=10 predicts various relations and constraints on higher order F^n couplings at different string loop levels on both sides. We prove the vanishing of two-loop corrections to the heterotic F^4 terms, which is one of the basic predictions from this duality. Furthermore, we show that the heterotic F^5 and (CP even) F^6 couplings are not renormalized at one loop. These results strengthen the conjecture that in D=10 any Tr F^(2n) coupling appears only at the disc tree-level on type I side and at (n-1)-loop level on the heterotic side. Our non-renormalization theorems are valid in any heterotic string vacuum with sixteen supercharges.