BI action for gravitational and electroweak fields

TL;DR

This paper proposes a generalized Born-Infeld action for electroweak and gravitational fields in four-dimensional spacetime, linking symmetry properties to physical parameters and recovering Einstein-Hilbert and Gauss-Bonnet actions in certain limits.

Contribution

It introduces a novel Born-Infeld type action incorporating Dirac matrices and covariant derivatives, with a symmetry postulate relating Lorentz transformations to electroweak potential.

Findings

Action reduces to Einstein-Hilbert and Gauss-Bonnet in linear and quadratic approximations.

Symmetry considerations connect Lorentz group parameters to electroweak potential.

The proposed framework unifies gravitational and electroweak fields within a generalized Born-Infeld structure.

Abstract

This note suggests a generalization of the Born--Infeld action (1932) on case of electroweak and gravitational fields in four-dimensional spacetime. The action is constructed from Dirac matrices, $\gamma_a$, and dimensionless covariant derivatives, $\pi_{a} = - i\ell \nabla_{a}$, where $\ell$ is of order of magnitude of Planck's length. By a postulate, the action possesses additional symmetry with respect to global transformations of the Lorentz group imposed on pairs ($\gamma_{a}$, $\pi_{a}$). It's shown, that parameter of the Lorentz group is associated with a constant value of the electroweak potential at spatial infinity. It follows, that in linear and quadratic in $\ell^2$ approximation, action for gravitational field coincides with Einstein-Hilbert (EH) and Gauss-Bonnet (GB).