On Matrix Geometry and Effective Actions

Abstract

We provide an elementary systematic discussion of single-trace matrix actions and of the group of matrix reparameterization that acts on them. The action of this group yields a generalized notion of gauge invariance which encompasses ordinary diffeomorphism and gauge invariances. We apply the formalism to non-abelian D-brane actions in arbitrary supergravity backgrounds, providing in particular explicit checks of the consistency of Myers' formulas with supergravity gauge invariances. We also draw interesting consequences for emergent space models based on the study of matrix effective actions. For example, in the case of the AdS_5XS^5 background, we explain how the standard tensor transformation laws of the supergravity fields under ordinary diffeomorphisms emerge from the D-instanton effective action in this background.

50 pages

References in corpus (7)

• On the covariance of the Dirac-Born-Infeld-Myers action
• More on closed string induced higher derivative interactions on D-branes
• Emergent Space and the Example of AdS_5XS^5
• Examples of Emergent Type IIB Backgrounds from Matrices
• Emergent D4-Brane Background from D-Particles
• Emergent D5-brane Background from D-strings
• The group structure of non-Abelian NS-NS transformations

Cited by in corpus (14)

• Non-Higgsable clusters for 4D F-theory models
• Gauge Theories, D-Branes and Holography
• D-Brane Probes in the Matrix Model
• Examples of Emergent Type IIB Backgrounds from Matrices
• SuperYang-Mills, Chern-Simons couplings and their all order ${\alpha }^{\prime }$ corrections in IIB superstring theory
• Emergent D4-Brane Background from D-Particles
• Emergent D5-brane Background from D-strings
• Gravity and On-Shell Probe Actions
• More on Ramond-Ramond, SYM, WZ couplings and their corrections in IIA
• Partial Gauge Fixing and Equivariant Cohomology
• D-instanton probe and the enhançon mechanism from a quiver gauge theory
• Non-perturbative aspects of gauge/gravity duality
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications
• Holographic backgrounds from D-brane probes