Poincare Invariance in Multiple D-brane Actions

TL;DR

This paper investigates how Poincare invariance constrains the form of multiple D-brane actions, leading to a series of correction terms and a unique Lorentz transformation rule for D0-branes, using new matrix-valued covariant objects.

Contribution

It introduces a method to determine all Poincare invariant structures in multiple D-brane actions and constructs new matrix-valued Lorentz covariant objects for this purpose.

Findings

Identifies an infinite series of correction terms constrained by Poincare invariance.

Proves the uniqueness of the Lorentz transformation rule for D0-brane coordinate matrices.

Develops new matrix-valued Lorentz covariant objects for invariant action construction.

Abstract

We show that the requirement of Poincare invariance (more specifically invariance under boosts/rotations that mix brane directions with transverse directions) places severe constraints on the form of actions describing multiple D-branes, determining an infinite series of correction terms to the currently known actions. For the case of D0-branes, we argue that up to field redefinitions, there is a unique Lorentz transformation rule for the coordinate matrices consistent with the Poincare algebra. We characterize all independent Poincare invariant structures by describing the leading term of each and providing an implicit construction of a Poincare invariant completion. Our construction employs new matrix-valued Lorentz covariant objects built from the coordinate matrices, which transform simply under the (extremely complicated) Lorentz transformation rule for the matrix coordinates.