A Unified Theory of Non-Linear Electrodynamics and Gravity

Understand

We describe a class of unified theories of electromagnetism and gravity.

• The Lagrangian is of the BF type, with a potential for the B-field, the gauge group is U(2) (complexified).
• Given a choice of the potential function the theory is a deformation of (complex) general relativity and electromagnetism, and describes just two propagating polarisations of the graviton and two of the photon.
• When gravity is switched off the theory becomes the usual non-linear electrodynamics with a general structure function.