Gauge theory of the de Sitter group and the Ashtekar formulation

Nieto, J. A.; Obregón, O.; Socorro, J.

doi:10.1103/physrevd.50.r3583

Cited by 40 publications

(75 citation statements)

References 17 publications

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“…The noncommutative signature and the Euler topological invariants are given by the real and imaginary parts of (28). For a Riemannian manifold, these topological invariants characterize gravitational instantons.…”

Section: Discussionmentioning

confidence: 99%

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Noncommutative topological theories of gravity

García‐Compeán¹,

Ramı́rez²,

Sabido³

et al. 2003

Phys. Rev. D

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The possibility of noncommutative topological gravity arising in the same manner as Yang-Mills theory is explored. We use the Seiberg-Witten map to construct such a theory based on a SL(2,C) complex connection, from which the Euler characteristic and the signature invariant are obtained. This gives us a way towards the description of noncommutative gravitational instantons as well as noncommutative local gravitational anomalies. * Electronic address: compean@fis.cinvestav.mx † Electronic address: octavio@ifug3.ugto.mx; Permanent adress:

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Section: Discussionmentioning

confidence: 99%

“…The action (15) arises naturally from the MacDowell-Mansouri type action [28]. A similar construction can be done for (2 + 1)-dimensional Chern-Simons gravity [29].…”

Section: Topological Gravitymentioning

confidence: 99%

Noncommutative topological theories of gravity

García‐Compeán¹,

Ramı́rez²,

Sabido³

et al. 2003

Phys. Rev. D

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“…For that purpose let us assume that the spacetime manifold M 2+10 can be broken up into the form M 10+2 → M 2+2 × M 0+8 . This implies that the SO(2, 10) Lovelock type curvature (see [12][13][14][15][16] and references therein)…”

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confidence: 99%

“…Let us now consider a MacDowell-Mansouri type action [13][14][15][16] in a 2 + 10-dimensional spacetime [17] …”

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confidence: 99%

Towards an Ashtekar formalism in 12 dimensions

Nieto

2007

Gen Relativ Gravit

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We discuss the Ashtekar formalism from the point of view of 12 dimensions. We first focus on the 2 + 10 spacetime signature and then we consider the transition 2 + 10 → (2 + 2) + (0 + 8). We argue that both sectors 2 + 2 and 0 + 8, which are exceptional signatures, can be analyzed from the point of view of a self-dual action associated with the Ashtekar formalism.Keywords Ashtekar theory · 12 dimensions · Two time physics Over the years it has become clear that considering gravitational and gauge theories with more than one time coordinate is a very interesting and useful idea for understanding different aspects of traditional gravitational and gauge field theories with only one time (see [1] and references therein). In particular, the 2 + 10-dimensional spacetime signature has emerged as an interesting possibility for the understanding of both supergravity and super Yang-Mills theory in D = 11 (see [2]). Thus, by seriously taking a 2 + 10-dimensional gravity one may be interested in various possibilities offered by this theory. For instance, one may be interested in a realistic theory in four-dimensions via the symmetry braking 2 + 10 → (1 + 3) + (1 + 7). However, this may not be the only attractive possibility. In fact, one may think on the alternative transition 2 + 10 → (2 + 2) + (0 + 8).(1) Dedicated to Octavio Obregón on the occasion of his 60th birthday.

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“…In this way, the de Sitter gauge theory comes up as the corrected Poincaré gauge theory. Alternatively, there are other approaches where de Sitter group based Yang-Mills theories are shown to be producing either Ashtekar formulation of gravity [11] or Einstein-Cartan version of general relativity [12].…”

Section: Introductionmentioning

confidence: 99%

Torsion, Scalar Field, Mass and FRW Cosmology

Mahato¹

2005

Int J Theor Phys

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In the Einstein-Cartan space U 4 , an axial vector torsion together with a scalar field connected to a local scale factor have been considered. By combining two particular terms from the SO(4, 1) Pontryagin density and then modifying it in a SO(3, 1) invariant way, we get a Lagrangian density with Lagrange multipliers. Then under FRW-cosmological background, where the scalar field is connected to the source of gravitation, the Euler-Lagrange equations ultimately give the constancy of the gravitational constant together with only three kinds of energy densities representing mass, radiation and cosmological constant. The gravitational constant has been found to be linked with the geometrical Nieh-Yan density.

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Gauge theory of the de Sitter group and the Ashtekar formulation

Abstract: By adding the Pontrjagin topological invariant to the gauge theory of the de Sitter group proposed by MacDowell and Mansouri we obtain an action quadratic in the fieldstrengths, of the Chern-Simons type, from which the Ashtekar formulation is derived.

Cited by 40 publications

References 17 publications

Noncommutative topological theories of gravity

Noncommutative topological theories of gravity

Towards an Ashtekar formalism in 12 dimensions

Torsion, Scalar Field, Mass and FRW Cosmology

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