Canonical approach to Courant brackets for D-branes

TL;DR

This paper extends the Courant bracket framework to Dp-branes, incorporating R-R couplings and revealing how gauge transformations and dualities like T-duality and S-duality are naturally encoded.

Contribution

It introduces a generalized Courant bracket for Dp-branes that includes R-R tensors and demonstrates how gauge transformations and dualities are embedded within this formalism.

Findings

Courant brackets for Dp-branes include R-R coupling tensors.

Gauge transformation rules derive from these brackets.

Manifest T-duality and S-duality in the formalism.

Abstract

We present an extension of the Courant bracket to the ones for Dp-branes by analyzing Hamiltonians and local superalgebras. Contrast to the basis of the bracket for a fundamental string which consists of the momentum and the winding modes, the ones for Dp-branes contain higher rank R-R coupling tensors. We show that the R-R gauge transformation rules are obtained by these Courant brackets for Dp-branes where the Dirac-Born-Infeld gauge field and the "two-vierbein field" play an essential role. Canonical analysis of the worldvolume theories naturally gives the basis of the brackets and the target space backgrounds keeping T-duality manifest at least for NS-NS sector. In a D3-brane analysis S-duality is manifest as a symmetry of interchanging the NS-NS coupling and the R-R coupling.