On Transgression Forms and Chern--Simons (Super)gravity
arXiv:hep-th/0512014
Abstract
A transgression form is proposed as lagrangian for a gauge field theory. The construction is first carried out for an arbitrary Lie Algebra g and then specialized to some particular cases. We exhibit the action, discuss its symmetries, write down the equations of motion and the boundary conditions that follow from it, and finally compute conserved charges. We also present a method, based on the iterative use of the Extended Cartan Homotopy Formula, which allows one to (i) systematically split the lagrangian in order to appropriately reflect the subspaces structure of the gauge algebra, and (ii) separate the lagrangian in bulk and boundary contributions. Chern--Simons Gravity and Supergravity are then used as examples to illustrate the method. In the end we discuss some further theoretical implications that arise naturally from the mathematical structure being considered.
18 pages, 1 figure. v2: two new appendices; v3: references added; v4: some improvement on the text, minor cosmetic changes
References in corpus (16)
- Black Hole Scan
- Dimensionally Continued Black Holes
- Conserved charges for gravity with locally AdS asymptotics
- Black holes with topologically nontrivial AdS asymptotics
- Conserved Charges for Even Dimensional Asymptotically AdS Gravity Theories
- Higher dimensional Chern-Simons supergravity
- Finite action principle for Chern-Simons AdS gravity
- A covariant formalism for Chern-Simons gravity
- Hoffmann-Infeld Black Hole Solutions in Lovelock Gravity
- Charges and Energy in Chern-Simons Theories and Lovelock Gravity
- Vacuum Energy in Odd-Dimensional AdS Gravity
- Higher dimensional gravity invariant under the AdS group
- Transgression forms as unifying principle in field theory
- Euler Chern Simons Gravity from Lovelock Born Infeld Gravity
- Covariant Lagrangian Formulation of Chern-Simons and BF Theories
- Intersecting hypersurfaces and Lovelock Gravity
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- Action Principles for Transgression and Chern-Simons AdS Gravities
- Alternative approach to the regularization of odd dimensional AdS gravity
- Transgression field theory at the interface of topological insulators
- Geometrical setting for the correspondence between gravity and Chern-Simons field theories