Duality in Yang’s theory of gravity

Abstract

The historical route and the current status of a curvature-squared model of gravity, in the affine form proposed by Yang, is briefly reviewed. Due to its inherent scale invariance, it enjoys some advantage for quantization, similarly as internal Yang-Mills fields. However, the exact vacuum solutions with double duality properties exhibit a 'vacuum degeneracy'. By modifying the duality via a scale breaking term, we demonstrate that only the Einstein equations with induced cosmological constant emerge for the classical background, even when coupled to matter sources.

Quantized gauge-affine gravity in the superfiber bundle approach

“…Then the supercurvature constraints are determined by the fact that the generalized supercurvature is an even tensorial 2-superform which leads to the determination of the gauge-affine gravity BRST and anti-BRST transformations. The obtained BRST transformations are nilpotent and equivalent to those given in [18,20,25]. Reducing the four-dimensional general affine group double-covering GA(4, R) to the Poincaré group double-covering ISO(1, 3) we have also found the BRST and anti-BRST transformations of the fields present in quantum Einstein gravity.…”

Spring Theory as an Approach to the Unification of Fields

“…Properties of these equations had been studied by various authors [6] [7] [8]. Pavelle [6] pointed out that Yang's pure space is non-physical unless the cosmological constant remains in Einstein's field equations which was later verified by Mielke [8]. We begin from the second Bianchi Identity…”

Torsion Wave Solutions in Yang-Mielke Theory of Gravity

“…There are many works devoted to the study of system (4), (5) in the special case (6) and one can get an idea of the historical development of the Yang-Mielke theory of gravity from the references stated in [11]. Further aspects of the history of this theory are also given in [14]. Detailed descriptions of the irreducible pieces of curvature and quadratic forms on curvature can be found in [10,15] and our previous work in this theory can be found in [11,[16][17][18], where much more information and references on the history and development of metric-affine gravity and known solutions of this theory can be found.…”