Higher Derivative Brane Couplings from T-Duality

TL;DR

This work addresses how higher-derivative four-derivative couplings between D-brane Wess-Zumino actions and NS-NS/RR fields are constrained by T-duality. By applying Buscher rules and assuming uncorrected NS-NS T-duality up to order $\alpha'^2$, the authors predict a set of extra four-derivative terms beyond the known $C^{(p-1)}$ piece, organized into $X^{(4)}$, $X^{(3)}$, and $X^{(2)}$ structures as in the fixed coupling expression. They then verify these predictions by computing disc amplitudes with one RR and two NS-NS insertions in multiple pictures, finding agreement with the T-duality results up to overall normalization and demonstrating picture-independence. The findings refine the brane WZ action at this order, with implications for local tadpole equations and flux vacua, and lay groundwork for a more complete, symmetry-respecting description including RR and B-field gauge invariances and potential anomaly inflow approaches. Overall, the paper strengthens the link between spacetime dualities and explicit worldsheet computations in determining brane couplings in string theory.

Abstract

The Wess-Zumino coupling on D-branes in string theory is known to receive higher derivative corrections which couple the Ramond-Ramond potential to terms involving the square of the spacetime curvature tensor. Consistency with T-duality implies that the branes should also have four-derivative couplings that involve the NS-NS B-field. We use T-duality to predict some of these couplings. We then confirm these results with string worldsheet computations by evaluating disc amplitudes with insertions of one R-R and two NS-NS vertex operators.

Figures (1)

• Figure 1: In these diagrams the wavy lines represent NS-NS fields while the solid lines represent R-R fields.