Yang-Mills, Gravity, and String Symmetries

Abstract

In this work we use constructs from the dual space of the semi-direct product of the Virasoro algebra and the affine Lie algebra of a circle to write a theory of gravitation which is a natural analogue of Yang-Mills theory. The theory provides a relation between quadratic differentials in 1+1 dimensions and rank two symmetric tensors in higher dimensions as well as a covariant local Lagrangian for two dimensional gravity. The isotropy equations of coadjoint orbits are interpreted as Gauss law constraints for a field theory in two dimensions, which enables us to extend to higher dimensions. The theory has a Newtonian limit in any space-time dimension. Our approach introduces a novel relationship between string theories and 2D field theories that might be useful in defining dual theories. We briefly discuss how this gravitational field couples to fermions.

To Appear in Phys. Lett. B, In memory of Emma Meurice

References in corpus (3)

• A Study of Fermions Coupled to Gauge and Gravitational Fields on a Cylinder
• Applications of W-algebras to BF theories, QCD and 4D Gravity
• A 2D Inspired 4D Theory of Gravity

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• Inflation from Dynamical Projective Connections
• Covariant and Manifestly Projective Invariant Formulation of Thomas-Whitehead Gravity
• General Coordinate Transformations as the Origins of Dark Energy
• Chiral Supergravitons Interacting with a 0-Brane N-Extended NSR Super-Virasoro Group
• The Research of Thomas P. Branson
• The Diffeomorphism Field Revisited