Yang-Mills, Gravity, and String Symmetries

TL;DR

This paper develops a gravity theory based on the dual space of certain algebraic structures, linking 2D and higher-dimensional tensors, and proposes a novel connection between string theories and 2D field theories.

Contribution

It introduces a new gravitational framework using algebraic constructs from the Virasoro and affine Lie algebras, establishing links between 2D and higher-dimensional theories and suggesting dualities with string theories.

Findings

Provides a covariant local Lagrangian for 2D gravity

Establishes a relation between quadratic differentials and higher-dimensional tensors

Suggests a new approach to string-field theory dualities

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.