On the exact quartic effective action for the type IIB superstring

TL;DR

This paper constructs an exact, SL(2,Z)-invariant four-point effective action for type IIB superstring theory, capturing known tree-level results, one-loop corrections, and non-perturbative D-instanton effects.

Contribution

It introduces a novel, explicit form of the quartic effective action that is fully invariant and includes both perturbative and non-perturbative corrections.

Findings

Reproduces known tree-level results.

Incorporates one-loop corrections in the NS-NS sector.

Includes non-perturbative D-instanton effects.

Abstract

We propose a four-point effective action for the graviton, antisymmetric two-forms, dilaton and axion of type IIB superstring in ten dimensions. It is explicitly SL(2,Z)-invariant and reproduces the known tree-level results. Perturbatively, it has only one-loop corrections for the NS-NS sector, generalizing the non-renormalization theorem of the R^4 term. Finally, the non-perturbative corrections are of the expected form, namely, they can be interpreted as arising from single D-instantons of multiple charge.