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Strong Homotopy Algebras in Noncommutative Gauge Theory and Higher Spin Gravity

Abstract

The modern problems of high energy physics call for more and more advanced mathematical concepts, among which noncommutative geometry and strong homotopy algebras seem come to the fore. The present project is aimed at developing and applying these general concepts to the construction of gauge theories on noncommutative spacetime manifolds or with noncommutative target-space geometry. Until now, these two classes of gauge theories, using essentially the same mathematics, have developed almost independently of each other. This project is supposed to create synergy between them. As specific applications, it is planned to consider noncommutative gauge theories on general symplectic-Riemannian manifolds, Chiral Higher Spin Gravity models, and massive higher spin fields. (AU)

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