Generally Covariant Actions for Multiple D-branes

Abstract

We develop a formalism that allows us to write actions for multiple D-branes with manifest general covariance. While the matrix coordinates of the D-branes have a complicated transformation law under coordinate transformations, we find that these may be promoted to (redundant) matrix fields on the transverse space with a simple covariant transformation law. Using these fields, we define a covariant distribution function (a matrix generalization of the delta function which describes the location of a single brane). The final actions take the form of an integral over the curved space of a scalar single-trace action built from the covariant matrix fields, tensors involving the metric, and the covariant distribution function. For diagonal matrices, the integral localizes to the positions of the individual branes, giving N copies of the single-brane action.

34 pages, LaTeX. v2: comments and refs added

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Cited by in corpus (17)

• Deformations of calibrated D-branes in flux generalized complex manifolds
• On the covariance of the Dirac-Born-Infeld-Myers action
• Fuzzy 5-spheres and pp-wave Matrix Actions
• Resolving brane collapse with 1/N corrections in non-Abelian DBI
• Giant Gravitons and Fuzzy CP^2
• Kappa-symmetry for coincident D-branes
• Quintessence and phantom dark energy from ghost D-branes
• On Matrix Geometry and Effective Actions
• Towards Quantum Dielectric Branes: Curvature Corrections in Abelian Beta Function and Nonabelian Born-Infeld Action
• Dielectric 5-Branes and Giant Gravitons in ABJM
• Electrified Fuzzy Spheres and Funnels in Curved Backgrounds
• Poincare Invariance in Multiple D-brane Actions
• Comparing two definitions for gauge variations of dielectric D-branes
• Gauge-Higgs Unification In Spontaneously Created Fuzzy Extra Dimensions
• Some thoughts about matrix coordinate transformations
• Holomorphically Covariant Matrix Models
• Action for N D0-Branes Invariant Under Gauged Galilean Transformations