A connection between linearized GaussBonnet gravity and classical electrodynamics II: Complete dual formulation
Abstract
In a recent publication, a procedure was developed which can be used to derive completely gauge invariant models from general Lagrangian densities with N order of derivatives and M rank of tensor potential. This procedure was then used to show that unique models follow for each order, namely classical electrodynamics for N = M = 1 and linearized GaussBonnet gravity for N = M = 2. In this paper, the nature of the connection between these two wellexplored physical models is further investigated by means of an additional common property; a complete dual formulation. First, we give a review of GaussBonnet gravity and the dual formulation of classical electrodynamics. The dual formulation of linearized GaussBonnet gravity is then developed. It is shown that the dual formulation of linearized GaussBonnet gravity is analogous to the homogenous half of Maxwell’s theory; both have equations of motion corresponding to the (second) Bianchi identity, built from the dual form of their respective field strength tensors. In order to have a dually symmetric counterpart analogous to the nonhomogenous half of Maxwell’s theory, the first invariant derived from the procedure in N = M = 2 can be introduced. The complete gauge invariance of a model with respect to Noether’s first theorem, and not just the equation of motion, is a necessary condition for this dual formulation. We show that this result can be generalized to the higher spin gauge theories, where the spinn curvature tensors for all N = M = n are the field strength tensors for each n. These completely gauge invariant models correspond to the Maxwelllike higher spin gauge theories whose equations of motion have been well explored in the literature.
 Publication:

International Journal of Modern Physics D
 Pub Date:
 2021
 DOI:
 10.1142/S0218271821500309
 arXiv:
 arXiv:2104.00988
 Bibcode:
 2021IJMPD..3050030B
 Keywords:

 Noether’s theorem;
 Gauss–Bonnet gravity;
 classical electrodynamics;
 gauge theory;
 General Relativity and Quantum Cosmology
 EPrint:
 26 pages