Gauge and Einstein Gravity from Non-Abelian Gauge Models on (original) (raw)

Gauge and Einstein gravity from non-abelian gauge models on noncommutative spaces

Physics Letters B, 2001

Following the formalism of enveloping algebras and star product calculus we formulate and analyze a model of gauge gravity on noncommutative spaces and examine the conditions of its equivalence to the general relativity theory. The corresponding Seiberg-Witten maps are established which allow the definition of respective dynamics for a finite number of gravitational gauge field components on noncommutative spaces.

A Noncommutative Extension of Gravity

International Journal of Modern Physics D, 1994

The commutative algebra of functions on a manifold is extended to a noncommutative algebra by considering its tensor product with the algebra of n×n complex matrices. Noncommutative geometry is used to formulate an extension of the Einstein-Hilbert action. The result is shown to be equivalent to the usual Kaluza-Klein theory with the manifold SUn as an internal space, in a truncated approximation.

Locally Anisotropic Supergravity and Gauge Gravity on Noncommutative Spaces

Noncommutative Structures in Mathematics and Physics, 2001

We outline the the geometry of locally anisotropic (la) superspaces and la-supergravity. The approach is backgrounded on the method of anholonomic superframes with associated nonlinear connection structure. Following the formalism of enveloping algebras and star product calculus we propose a model of gauge la-gravity on noncommutative spaces. The corresponding Seiberg-Witten maps are established which allow the definition of dynamics for a finite number of gravitational gauge field components on noncommutative spaces. *

Lie algebraic noncommutative gravity

Physical Review D, 2007

We exploit the Seiberg -- Witten map technique to formulate the theory of gravity defined on a Lie algebraic noncommutative space time. Detailed expressions of the Seiberg -- Witten maps for the gauge parameters, gauge potentials and the field strengths have been worked out. Our results demonstrate that notwithstanding the introduction of more general noncommutative structure there is no first order correction, exactly as happens for a canonical (i.e. constant) noncommutativity.

Some Remarks on Gravity in Noncommutative Spacetime and a New Solution to the Structure Equations

2003

In this paper, starting from the common foundation of Connes' noncommutative geometry (NCG) [1,2,3,4], various possible alternatives in the formulation of a theory of gravity in noncommutative spacetime are discussed in detail. The diversity in the final physical content of the theory is shown to the the consequence of the arbitrariness in each construction steps. As an alternative in the last step, when the staructure equations are to be solved, a minimal set of constraints on the torsion and connection is found to determine all the geometric notions in terms of metric. In the Connes-Lott model of noncommutative spacetime, in order to keep the full spectrum of the discretized Kaluza-Klein theory [5], it is necessary to include the torsion in the generalized Einstein-Hilbert-Cartan action.

Noncommutativity in the Theory of Gravity

Noncommutative gravity is a very interesting subject that has not yet been successfully related to string theory. However, it can be motivated by itself by the consideration of a description of the microscopic structure of spacetime, leaving for the future its precise connection to string theory or M-theory. In this paper we review some of the recent attempts to make sense of the noncommutative description of some classical theories of gravity by using the Seiberg-Witten map. In particular we describe noncommutative topological gravity and a gauge invariant proposal generalizing Plebański-Ashtekar Self-dual gravity.

Noncommutative Spacetime and Emergent Gravity

Bulg.J.Phys.35 (2008) 323-328, 2007

We argue that a field theory defined on noncommutative (NC) spacetime should be regarded as a theory of gravity, which we refer to as the emergent gravity. A whole point of the emergent gravity is essentially originated from the basic property: A NC spacetime is a (NC) phase space. This fact leads to two important consequences: (I) A NC field theory can basically be identified with a matrix model or a large N field theory where NC fields can be regarded as master fields of large N matrices. (II) NC fields essentially define vector (tetrad) fields. So they define a gravitational metric of some manifold as an emergent geometry from NC gauge fields. Of course, the pictures (I) and (II) should refer to the same physics, which should be familiar with the large N duality in string theory. The 1/N corrections in the picture (I) correspond to the derivative corrections in terms of the noncommutativity \theta for the picture (II).