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Generally covariant actions for systems of multiple DO-branes Ling, Henry Ho-Kong

Abstract

This thesis focuses on understanding how general coordinate invariance can be incorporated into effective actions for systems of many D0-branes coupled to bulk supergravity fields. We present progress in two special cases. First, we discuss the implementation of covariance under arbitrary spatial diffeomorphisms. A method of constructing actions with manifest covariance under these diffeomorphisms is developed. While the matrix D0-branes coordinates transform in a complicated manner under spatial diffeomorphisms, we find that it is possible to replace these with matrix-valued fields in space with a simple vector transformation law. Using this vector field, we define a distribution function that serves as a matrix generalization of the delta function, and which describes the location of the D0-branes. The covariant Lagrangians then take the form of an integral over space of a scalar built from the various fields times the matrix distribution function. Next, we approach the problem of implementing covariance under coordinate transformations that mix the space and time directions. As a first step towards understanding this problem, we consider in detail the simpler case of incorporating Poincaré invariance into actions for multiple D0-branes in Minkowski space. We find evidence for a non-trivial Lorentz transformation rule for the matrix D0-brane coordinates by using the Poincaré algebra as a guiding consistency condition. We determine the necessary conditions that must be satisfied by the leading term of any Poincaré invariant action, and find an implicit method of constructing a Poincaré invariant completion of any such leading term. The approach is based on using matrix-valued Lorentz covariant fields defined on space-time, built from the matrix D0-brane coordinates.

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