A 2D Inspired 4D Theory of Gravity

TL;DR

This paper proposes a novel 4D gravity theory inspired by 2D geometric actions, introducing a (1,3) pseudo tensor as a dynamical variable, and explores its classical coupling to matter.

Contribution

It introduces a new 4D gravitational framework based on 2D geometric actions, utilizing a (1,3) pseudo tensor to extend the theory beyond traditional quadratic differentials.

Findings

Proposes a 4D gravity model linked to 2D theories.

Introduces a (1,3) pseudo tensor as a dynamical variable.

Discusses classical matter coupling in the new framework.

Abstract

Coadjoint orbits of the Virasoro and Kac-Moody algebras provide geometric actions for matter coupled to gravity and gauge fields in two dimensions. However, the Gauss' law constraints that arise from these actions are not necessarily endemic to two-dimensional topologies. Indeed the constraints associated with Yang-Mills naturally arise from the coadjoint orbit construction of the WZW model. One may in fact use a Yang-Mills theory to provide dynamics to the otherwise fixed coadjoint vectors that define the orbits. In this letter we would like to exhibit an analogue of the Yang-Mills classical action for the diffeomorphism sector. With this analogue one may postulate a 4D theory of gravitation that is related to an underlying two dimensional theory. Instead of quadratic differentials, a (1,3) pseudo tensor becomes the dynamical variable. We briefly discuss how this tensor may be classically coupled to matter.