Yang-Mills, Gravity, and 2D String Symmetries (original) (raw)

Yang-Mills, gravity, and string symmetries

Physics Letters B, 1997

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.

Higher Gauge Theory and Gravity in 2+1 Dimensions

International Journal of Modern Physics A, 2007

Non-Abelian higher gauge theory has recently emerged as a generalization of standard gauge theory to higher-dimensional (two-dimensional in the present context) connection forms, and as such, it has been successfully applied to the non-Abelian generalizations of the Yang–Mills theory and 2-form electrodynamics. (2+1)-dimensional gravity, on the other hand, has been a fertile testing ground for many concepts related to classical and quantum gravity, and it is therefore only natural to investigate whether we can find an application of higher gauge theory in this latter context. In the present paper we investigate the possibility of applying the formalism of higher gauge theory to gravity in 2+1 dimensions, and we show that a nontrivial model of (2+1)-dimensional gravity coupled to scalar and tensorial matter fields — the ΣΦEA model — can be formulated as a higher gauge theory (as well as a standard gauge theory). Since the model has a very rich structure — it admits as solutions black...

General Relativity as a (constrained) Yang-Mills's Theory and a Novel Gravity with Torsion

2000

We show that General Relativity (GR) with cosmological constant may be formulated as a rather simple constrained SO(D-1,2) (or SO(D,1))-Yang-Mills (YM) theory. Furthermore, the spin connections of the Cartan-Einstein formulation for GR appear as solutions of a genuine SO(D-1,1)-YM. We also present a theory of gravity with torsion as the most natural extension of this result. The theory comes out to be strictly an YM-theory upon relaxation of a suitable constraint. This work sets out to enforce the close connection between YM theories and GR by means of a new construction.

Higher-dimensional gravity, propagating torsion and AdS gauge invariance

Classical and Quantum Gravity, 2000

The most general theory of gravity in d dimensions which leads to second order field equations for the metric has [(d − 1)/2] free parameters. It is shown that requiring the theory to have the maximum possible number of degrees of freedom, fixes these parameters in terms of the gravitational and the cosmological constants. In odd dimensions, the Lagrangian is a Chern-Simons form for the (A)dS or Poincaré groups. In even dimensions, the action has a Born-Infeld-like form.

General Relativity as a (Constrained) Yang-Mills Theory and a Novel Gravity with Torsion

General Relativity and Gravitation, 2002

We show that General Relativity (GR) with cosmological constant may be formulated as a rather simple constrained SO(D − 1, 2) (or SO(D, 1))-Yang-Mills (YM) theory. Furthermore, the spin connections of the Cartan-Einstein formulation for GR appear as solutions of a genuine SO(D−1, 1)-YM. We also present a theory of gravity with torsion as the most natural extension of this result. The theory comes out to be strictly an YM-theory upon relaxation of a suitable constraint. This work sets out to enforce the close connection between YM theories and GR by means of a new construction.

Yang-Mills model for centrally extended 2D gravity

Physical Review D, 2022

A Yang-Mills theory linear in the scalar curvature for 2d gravity with symmetry generated by the semidirect product formed with the Lie derivative of the algebra of diffeomorphisms with the two-dimensional Abelian algebra is formulated. As compared with dilaton models, the rôle of the dilaton is played by the dual field strength of a U (1) gauge field. All vacuum solutions are found. They have constant scalar curvature and constant dual field strength. In particular, solutions with vanishing cosmological constant but nonzero scalar curvature exist. In the conformal-Lorenz gauge, the model has a CFT interpretation whose residual symmetry combines holomorphic diffeomorphisms with a subclass of U (1) gauge transformations while preserving dS 2 and AdS 2 boundary conditions. This is the same symmetry as in the Jackiw-Teitelboim-Maxwell considered by Hartman and Strominger. It is argued that this is the only nontrivial Yang-Mills model linear in the scalar curvature that exists for real Lie algebras of dimension four.

A Yang-Mills model for centrally extended 2d gravity

2021

A Yang-Mills theory linear in the scalar curvature for 2d gravity with symmetry generated by the semidirect product formed with the Lie derivative of the algebra of diffeomorphisms with the two-dimensional Abelian algebra is formulated. As compared with dilaton models, the rôle of the dilaton is played by the dual field strength of a U(1) gauge field. All vacuum solutions are found. They have constant scalar curvature and constant dual field strength. In particular, solutions with vanishing cosmological constant but nonzero scalar curvature exist. In the conformal-Lorenz gauge, the model has a CFT interpretation whose residual symmetry combines holomorphic diffeomorphisms with a subclass of U(1) gauge transformations while preserving dS2 and AdS2 boundary conditions. This is the same symmetry as in the Jackiw-Teitelboim-Maxwell considered by Hartman and Strominger. It is argued that this is the only nontrivial Yang-Mills model linear in the scalar curvature that exists for real Lie ...

4-dimensional General Relativity from the instrinsic spatial geometry of Yang–Mills theory

Nuclear Physics B, 2011

In this paper we derive 4-dimensional General Relativity from three dimensions, using the intrinsic spatial geometry inherent in Yang-Mills theory which has been exposed by previous authors as well as as some properties of the Ashtekar variables. We provide various interesting relations, including the fact that General Relativity can be written as a Yang-Mills theory where the antiself-dual Weyl curvature replaces the Yang-Mills coupling constant. We have generalized the results of some previous authors, covering Einsteins spaces, to include more general spacetime geometries.

Generalized two-dimensional Yang-Mills theory is a matrix string theory

Nuclear Physics B - Proceedings Supplements, 2000

We consider two-dimensional Yang-Mills theories on arbitrary Riemann surfaces. We introduce a generalized Yang-Mills action, which coincides with the ordinary one on flat surfaces but differs from it in its coupling to two-dimensional gravity. The quantization of this theory in the unitary gauge can be consistently performed taking into account all the topological sectors arising from the gauge-fixing procedure. The resulting theory is naturally interpreted as a Matrix String Theory, that is as a theory of covering maps from a two-dimensional world-sheet to the target Riemann surface.

Generalized Yang-Mills theory and gravity

Physical Review D, 2016

We propose a generalization of Yang-Mills theory for which the symmetry algebra does not have to be factorized as mutually commuting algebras of a finite-dimensional Lie algebra and the algebra of functions on base space. The algebra of diffeomorphism can be constructed as an example, and a class of gravity theories can be interpreted as generalized Yang-Mills theories. These theories in general include a graviton, a dilaton and a rank-2 antisymmetric field, although Einstein gravity is also included as a special case. We present calculations suggesting that the connection in scattering amplitudes between Yang-Mills theory and gravity via BCJ duality can be made more manifest in this formulation.