# Twisted covariant noncommutative self-dual gravity

@article{EstradaJimnez2008TwistedCN, title={Twisted covariant noncommutative self-dual gravity}, author={Sendic Estrada‐Jim{\'e}nez and Hugo Garc{\'i}a-Compe{\'a}n and Octavio Obreg{\'o}n and Carlos Ram{\'i}rez}, journal={Physical Review D}, year={2008}, volume={78}, pages={124008} }

A twisted covariant formulation of noncommutative self-dual gravity is presented. The formulation for constructing twisted noncommutative Yang-Mills theories is used. It is shown that the noncommutative torsion is solved at any order of the {theta} expansion in terms of the tetrad and some extra fields of the theory. In the process the first order expansion in {theta} for the Plebanski action is explicitly obtained.

## 22 Citations

### Noncommutative D=4 gravity coupled to fermions

- Mathematics
- 2009

We present a noncommutative extension of Einstein-Hilbert gravity in the context of twist-deformed space-time, with a -product associated to a quite general triangular Drinfeld twist. In particular…

### Noncommutative gravity with self-dual variables

- PhysicsClassical and Quantum Gravity
- 2018

We build a noncommutative extension of Palatini–Holst theory on a twist-deformed spacetime, generalizing a model that has been previously proposed by Aschieri and Castellani. The twist deformation…

### Noncommutativity, Cosmology and Λ

- Mathematics
- 2012

The effects of phase space deformations in standard scalar field cosmology are studied. The deformation is introduced by modifying the symplectic structure of the minisuperspace variables to have a…

### Noncommutative gravity coupled to fermions: second order expansion via Seiberg-Witten map

- PhysicsJournal of High Energy Physics
- 2012

We use the Seiberg-Witten map (SW map) to expand noncommutative gravity coupled to fermions in terms of ordinary commuting fields. The action is invariant under general coordinate transformations and…

### Noncommutative gravity coupled to fermions: second order expansion via Seiberg-Witten map

- Physics
- 2012

A bstractWe use the Seiberg-Witten map (SW map) to expand noncommutative gravity coupled to fermions in terms of ordinary commuting fields. The action is invariant under general coordinate…

### OSp(1|4) supergravity and its noncommutative extension

- Physics, Mathematics
- 2013

We review the OSp(1|4)-invariant formulation of N=1, D=4 supergravity and present its noncommutative extension, based on a star-product originating from an abelian twist with deformation parameter…

### Projective module description of embedded noncommutative spaces

- Mathematics
- 2008

An algebraic formulation is given for the embedded noncommutative spaces over the Moyal algebra developed in a geometric framework in \cite{CTZZ}. We explicitly construct the projective modules…

### Two roads to noncommutative causality

- Mathematics
- 2015

We review the physical motivations and the mathematical results obtained so far in the isocone-based approach to noncommutative causality. We also give a briefer account of the alternative framework…

### Noncommutative Supergravity

- Physics
- 2011

We present a noncommutative extension of ﬁrst order Einstein-Hilbert gravity in the context of twist-deformed space-time, with a ? -product associated to a triangular Drinfeld twist. In particular…

## References

SHOWING 1-10 OF 30 REFERENCES

### Nonabelian Gauge Theories on Noncommutative Spaces

- Mathematics
- 2001

In this paper, we describe a method for obtaining the nonabelian Seiberg-Witten map for any gauge group and to any order in θ. The equations defining the Seiberg-Witten map are expressed using a…

### Twisted Gauge Theories

- Mathematics
- 2006

Gauge theories on a space-time that is deformed by the Moyal–Weyl product are constructed by twisting the coproduct for gauge transformations. This way a deformed Leibniz rule is obtained, which is…

### Noncommutative perturbative dynamics

- Physics
- 2000

We study the perturbative dynamics of noncommutative field theories on R d , and find an intriguing mixing of the UV and the IR. High energies of virtual particles in loops produce non-analyticity at…

### Deformed Gauge Theories

- Mathematics
- 2006

Gauge theories are studied on a space of functions with the Moyal-Weyl product. The development of these ideas follows the differential geometry of the usual gauge theories, but several changes are…

### Twist to Close

- Mathematics
- 2006

It has been proposed that the Poincare and some other symmetries of noncommutative field theories should be twisted. Here we extend this idea to gauge transformations and find that twisted gauge…

### Nonabelian Gauge Theories on Noncommutative Spaces

- Mathematics
- 2002

A formalism is presented where gauge theories for nonabelian groups can be constructed on a noncommutative algebra.

### SL(2,R)-Symmetry and Noncommutative Phase Space in (2+2) Dimensions

- Mathematics
- 2008

We generalize the connection between 2t physics and noncommutative geometry. In particular, we apply our formalism to a target spacetime of signature (2+2). Specifically, we compute an algebra of a…

### Deformed Bialgebra of Diffeomorphisms

- Mathematics
- 2004

The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates is represented by differential operators on noncommutative spaces. The algebra remains…

### Elements of Noncommutative Geometry

- Mathematics
- 2000

This volume covers a wide range of topics including sources of noncommutative geometry; fundamentals of noncommutative topology; K-theory and Morita equivalance; noncommutative integrodifferential…

### Noncommutative Geometry

- Mathematics
- 1997

Noncommutative Spaces It was noticed a long time ago that various properties of sets of points can be restated in terms of properties of certain commutative rings of functions over those sets. In…