Born–Infeld Gravity from the MacDowell–Mansouri Action and Its Associated β-Term

• Published in: Advances in applied Clifford algebras 2019-04, Vol.29 (2), p.1-11, Article 24
• Main Authors: López, J. L., Obregón, O., Ortega-Cruz, M.
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Born-Infeld theory; Gauge theory; Gravitation; Homage to Prof. W.A. Rodrigues Jr; Mathematical and Computational Physics; Mathematical Methods in Physics; Physics; Physics and Astronomy; Theoretical; Yang-Mills theory
• ISSN: 0188-7009; 1661-4909
• DOI: 10.1007/s00006-019-0940-9

In this work a generalization of a Born–Infeld theory of gravity with a topological β -term is proposed. These type of Born–Infeld actions were found from the theory introduced by MacDowell and Mansouri. This theory known as MacDowell–Mansouri (MM) gravity was one of the first attempts to construct a gauge theory of gravitation, and within this framework it was introduced in the action a topological β -term relevant for quantization purposes in an analogous way as in Yang–Mills theory. By the use of the self-dual and antiself-dual actions of MM gravity, we further define a Born–Infeld gravity generalization corresponding to MM gravity with the β -term.