D-Brane Effective Lagrangian in Spacetimes with Boundaries

TL;DR

This paper derives higher-derivative corrections to the D-brane effective Lagrangian in spacetimes with boundaries, ensuring T-duality invariance and including boundary extrinsic curvature effects, up to eighth order in field strength.

Contribution

It provides the most general form of the bulk and boundary D-brane Lagrangian consistent with T-duality, including 49 couplings and boundary extrinsic curvature terms.

Findings

Bulk Lagrangian satisfies T-duality without residual total derivatives.

Determined 49 couplings in the bulk Lagrangian, with 2 physical parameters from S-matrix.

Extended the DBI Lagrangian to include boundary extrinsic curvature.

Abstract

In this study, we explore the transformation of $D_p$-branes to $D_{p-1}$-branes under T-duality when the $D$-brane is embedded in a spacetime with a boundary. Our goal is to derive the higher-derivative corrections to the Dirac-Born-Infeld (DBI) Lagrangian for both the bulk and boundary terms. For the bulk terms, we calculate the $\alpha'$ corrections for the massless open string fields, up to the 8th order in the dimensionless Maxwell field strength. We demonstrate that the bulk Lagrangian can satisfy the T-duality constraint without residual total derivative terms in the base space. This determines the most general independent couplings of the massless open string fields in the bulk Lagrangian, encompassing 145 coupling constants, up to three parameters. Two of these parameters are physical and are determined by disk-level S-matrix elements, while the third is unphysical and can be eliminated by field redefinitions and integration by parts. The final result for the bulk Lagrangian consists of 49 couplings. For the boundary terms, applying T-duality symmetry to the massless open string field allows us to extend the DBI Lagrangian to incorporate the extrinsic curvature of the boundary.