Derivative corrections to the D-brane Born-Infeld action: non-geodesic embeddings and the Seiberg-Witten map

TL;DR

This paper derives higher-derivative corrections to D-brane actions, explores their geometric embedding properties, and analyzes their behavior under the Seiberg-Witten map, enhancing understanding of D-brane effective theories.

Contribution

It provides explicit dimensional reductions of four-derivative corrections for D-branes and examines their transformation under the Seiberg-Witten map, including non-geodesic embeddings.

Findings

Derived lower-dimensional Dp-brane corrections involving second fundamental form

Analyzed non-commutative transformation properties of corrections

Discussed potential higher-order derivative terms

Abstract

We dimensionally reduce the four-derivative corrections to the parity-conserving part of the D9-brane effective action involving all orders of the gauge field, to obtain corrections to the actions for the lower-dimensional Dp-branes. These corrections involve the second fundamental form and correspond to a non-geodesic embedding of the Dp-brane into (flat) ten-dimensional space. In addition, we study the transformation of the corrections under the Seiberg-Witten map relating the ordinary and non-commutative theories. A speculative discussion about the higher-order terms in the derivative expansion is also included.