A pedagogical review of gravity as a gauge theory

Abstract

After reviewing how Albert Einstein's general relativity (GR) can be viewed as a gauge theory of the Poincaré algebra, we show how Élie Cartan's geometric formulation of Newtonian gravity (Newton-Cartan gravity) can be viewed as a gauge theory of the Bargmann algebra following the construction of [R. Andringa, E. Bergshoeff, S. Panda, and M. de Roo, "Newtonian Gravity and the Bargmann Algebra," Class. Quant. Grav. 28 (2011) 105011, arXiv:1011.1145 [hep-th]]. In doing so, we will touch on the following auxiliary topics: the extension of Yang-Mills gauge theory to a more generic formalism of gauge theory, the fiber bundle picture of gauge theory along with the soldering procedure necessary to complete the gravity as a gauge theory picture, the vielbein formalism of GR, Lie algebra procedures such as central extensions and İnönü-Wigner contractions, and the hallmarks of Newtonian gravity which differentiate it from GR. The objective of the present work is to pedagogically fill in the gaps between the above citation and an undergraduate physics and mathematics education. Working knowledge of GR and some familiarity with classical field theory and Lie algebras is assumed.

References in corpus (9)

• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Newtonian Gravity and the Bargmann Algebra
• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• Thermal Hall Effect and Geometry with Torsion
• Extended Galilean symmetries of non-relativistic strings
• From Rigid Supersymmetry to Twisted Holomorphic Theories
• Newton-Cartan Gravity and Torsion
• The Galilean Superstring
• Newton-Cartan Gravity in Noninertial Reference Frames