Constraining the D3-brane effective action

TL;DR

This paper investigates higher derivative corrections in the D3-brane effective action, showing they are protected and receive limited perturbative and non-perturbative contributions, with proposed modular form expressions.

Contribution

It provides new insights into the protected nature of D^{2k} R^2 interactions and proposes explicit modular form expressions for their coefficients.

Findings

Interactions are protected for small k

Coefficients receive finite perturbative contributions

Non-perturbative D-instanton contributions are included

Abstract

We consider higher derivative corrections of the type D^{2k} R^2 in the effective action of the D3-brane with trivial normal bundle. Based on the perturbative disc and annulus amplitudes, and constraints of supersymmetry and duality, we argue that these interactions are protected, at least for small values of k. Their coefficient functions receive only a finite number of perturbative contributions, and non-perturbative contributions from D-instantons. We propose expressions for these modular forms for low values of k.