Construction of $R^4$ Terms in N=2 D=8 Superspace

TL;DR

This paper constructs $R^4$ terms in the N=2 D=8 superspace for Type II superstring compactified on $T^2$, providing a simple proof of their non-renormalization theorems.

Contribution

It introduces a method to construct $R^4$ terms using linearized superfields in N=2 D=8 superspace, confirming non-renormalization properties.

Findings

Explicit construction of $R^4$ terms in superspace

Proof of $R^4$ non-renormalization theorems

Simplification of previous conjectures

Abstract

Using linearized superfields, $R^4$ terms in the Type II superstring effective action compactified on $T^2$ are constructed as integrals in N=2 D=8 superspace. The structure of these superspace integrals allows a simple proof of the $R^4$ non-renormalization theorems which were first conjectured by Green and Gutperle.