Brane Mechanics

Brane mechanics is the study of the dynamics of relativistic extended objects [1,2], like relativistic strings, domain walls, and objects of higher dimension. In a relativistic setting, branes describe physical systems with degrees of freedom localized on spacelike sub-manifolds in an ambient fixed background spacetime, or ‘‘bulk". The organizing principle of brane mechanics is the symmetry of reparametrization invariance. Branes are described by a reparametrization invariant local action that is a functional of the geometry of the worldvolume spanned by the brane in its evolution. Reparametrization invariance and the background diffeomorphism invariance or Poincaré invariance for a Minkowski background, limit strongly the number of possible geometric models available. Besides its importance in relativistic mechanics, brane mechanics is of interest in a variety of contexts.

Brane mechanics plays an essential role in the framework of brane worlds scenarios, where the four-dimensional universe is considered as a brane embedded in a higher dimensional fixed background, curved or flat, see e.g. [3] and references therein, and in M-theory, where branes are considered as fundamental objects, see e.g. [4]. Other applications in the realm of astrophysics and black hole physics where physical degrees of freedom are localized on submanifolds of spacetime can also be listed. An additional recent motivation comes from the study of entangling surfaces, and the general subject of boundary entropy [5–7].

References

[1] B. Carter, Internat. J. Theoret. Phys. 40 (2001) 2099.

[2] R. Capovilla, J. Guven, Phys. Rev. D 51 (1994) 6736.

[3] R. Martens, K. Koyama, Living Rev. Relativ. 7 (2010) 7.

[4] J. Simon, Living Rev. Relativ. 15 (2012) 3.

[5] J. Armas J, J. Tarrío, J. High Energy Phys. 04 (2018) 100.

[6] E. Engelhardt, E. Fischetti, Surface Theory: the Classical, the Quantum, and the Holographic arXiv:1904.08423.

[7] A.J. Speranza, Geometrical tools for embedding fields, submanifolds, and foliations arXiv:1904.08012v2.

“In order to make an apple pie from scratch, you must first create the universe.”

Carl Sagan