Couplings of order six in the gauge field strength and the second fundamental form on a D$_p$-brane at order $\alpha'^2$

TL;DR

This paper determines all gauge-invariant couplings involving gauge field strength and second fundamental form on Dp-branes at order α'^2, using T-duality constraints, and confirms consistency with existing literature.

Contribution

It systematically finds and constrains 146 independent couplings at order α'^2 on Dp-branes using T-duality, extending previous partial results.

Findings

Identified 12+146 independent couplings at order α'^2.

T-duality constrains 150 of these couplings.

Remaining 8 couplings fixed by comparison with literature.

Abstract

Using the assumption that the independent gauge invariant couplings on the world-volume of the non-perturbative objects in the string theory are independent of the background, we find the four and the six gauge field strength and/or the second fundamental form couplings on the world volume of a D$_p$-brane in the superstring theory at order $\alpha'^2$ in the normalization that $F$ is dimensionless. We have found them by considering the particular background which has one circle and by imposing the corresponding T-duality constraint on the independent couplings. In particular, we find that there are 12+146 independent gauge invariant couplings at this order, and the T-duality constraint can fix 150 of them. We show that these couplings are fully consistent with the partial results in the literature. This comparison also fixes the remaining 8 couplings.