Chiral splitting and world-sheet gravitinos in higher-derivative string amplitudes

TL;DR

This paper advances the construction of higher-derivative superinvariants in ten-dimensional type-II string theories, revealing new features in string amplitude calculations, including the importance of worldsheet gravitino zero modes and unexpected fermionic correlator relations.

Contribution

It introduces novel methods for constructing higher-derivative superinvariants, emphasizing the role of chiral splitting and worldsheet gravitino zero modes in string amplitude computations.

Findings

New relations between fermionic correlators

Necessity of worldsheet gravitino zero modes in vertex operators

Discrepancy with predictions from the linear scalar superfield

Abstract

We report on progress made in the construction of higher-derivative superinvariants for type-II theories in ten dimensions. The string amplitude calculations required for this analysis exhibit interesting features which have received little attention in the literature so far. We discuss two examples from a forthcoming publication: the construction of the (H_{NS})^2 R^3 terms and the fermionic completion of the \epsilon\epsilon R^4 terms. We show that a correct answer requires very careful treatment of the chiral splitting theorem, implies unexpected new relations between fermionic correlators, and most interestingly, necessitates the use of worldsheet gravitino zero modes in the string vertex operators. In addition, we discuss the relation of our results to the predictions of the linear scalar superfield of the type-IIB theory and find (and explain) an interesting discrepancy.