Heterotic versus Type I

TL;DR

This paper compares heterotic and type-I string theory calculations of specific higher-derivative terms, clarifying D-brane instanton contributions and their relation to duality and matrix model elliptic genera.

Contribution

It provides a detailed comparison of $F^4$ and $R^4$ terms in heterotic and type-I theories, revealing rules for D-brane instanton effects and their mathematical representation.

Findings

D-branes do not run in loops.

Instanton contributions originate from orbifold fixed points.

Instanton sums relate to elliptic genera of matrix models.

Abstract

I compare the calculations of special $F^4$ and $R^4$ terms in the (toroidally-compactified) heterotic and type-I effective actions. Besides checking duality, this elucidates the quantitative rules of D-brane calculus. I explain in particular (a) why D-branes do not run in loops, and (b) how their instanton contributions arise from orbifold fixed points of their moduli space. The instanton sum has a simple representation as a sum of the elliptic genera of matrix models.